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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
An open wooden box 80 cm long, 65 cm wide and 45 cm high, is made of 2.5 cm thick wood. Find (i) the capacity of the box, (ii) volume of wood used and (iii) weight of the box, it being givne that 100 `cm^(3)` of wood weight 8g |
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Answer» External length of the box = 80 cm External breadth of the box = 65 cm External height of the box = 45 cm External volume of the box = `(80 xx 65 xx 45)` cu cm `= 234000 cm^(3)` Internal length of the box `= [80 - (2.5 xx 2)] cm = (80 -5)cm` = 75 cm Internal breadth of the box `= [65 - (2.5 xx 2)] cm = (65-5) cm` = 60 cm Internal height of the box `== (45 - 2.5) cm = 42.5 cm` (i) Capacity of the box = internal volume of the box `= (75 xx 60 xx 42.5) cm^(3) = 191250 cm^(3)` (ii) Volume of wood used = (external volume) - (internal volume) `= (234000 - 191250) cm^(3) = 42750 cm^(3)` Weight of `100 cm^(3)` of wood = 8g Weight of `42750 cm^(3)` of wood `= ((8)/(100) xx 42750) g = 3420 g` = 3 kg 420 g |
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| 2. |
How many bricks will be required to construct a wall 13.5 m long, 6 m high and 22.5 cm thick ? It is being given that each brick measured `(27 cm xx 12.5 cm xx 9 cm)` ? |
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Answer» Length of the wall `= (13.5 xx 100) cm = 1350 cm` Breadth of the wall = 22.5 cm Height of the wall `= (6 xx 100) cm = 600 cm` Volume of the wall `= (1350 xx 22.5 xx 600) cm^(3)` Volume of each brick `= (27 xx 12.5 xx 9) cm^(3)` Number of bricks required `= (("volume of the wall")/("volume of 1 brick"))` `= ((1350 xx 22.5 xx 600)/(27 xx 12.5 xx 9)) = 6000` |
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| 3. |
How many planks of dimensions `(5m xx 25 cm xx 10 cm)` can be stored in a pit which is 20m long, 6m wide and 80 cm deep ? |
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Answer» Correct Answer - 768 Volume of pit `= (20 xx 6 xx (80)/(100)) m^(3) = 96 m^(3)` Volume of one plank `= (5 xx (25)/(100) xx (10)/(100)) m^(3) = (1)/(8) m^(3)` Number of planks `= ("volume of pit")/("volume of 1 plank")` |
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| 4. |
How many bricks will be required to construct a wall 8m long, 6m high and 22.5 cm thick if each brick measures `(25 cm xx 11.25 cm xx 6 cm)` ? |
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Answer» Correct Answer - 6400 Required number of bricks `= ("volume of the wall in "cm^(3))/("volume of 1 brick in "cm^(3))` `= (800 xx 600 xx 22.5)/(25 xx 11.25 xx 6)` |
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| 5. |
a hemispherical bowl is made of steel 0.5 cm thick. The inside radius of the bowl is 4 cm. Find the volume of steel used in making the bowl. |
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Answer» Correct Answer - `56.83 cm^(3)` Inner radius , r = 4 cm, and outer radius, R = 4.5 cm Volume of steel `= (2)/(3) pi xx [(4.5)^(3) - (4)^(3)] cm^(3) = 56.83 cm^(3)` |
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| 6. |
Rainwater, which falls on a flat rectangular rooftop of dimensions 22m by 10m, is transferred into a cylindrical vessel of internal radius 50 cm through a circular pipe. A certain day recorded a rainfall of 2.5 cm. Find the (i) volume and (ii) height of the water, filled in the cylindrical vessel. |
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Answer» (i) Volume of water filled in the cylindrical vessel = volume of water collected on the rooftop `= (22 xx 10 xx (2.5)/(100)) m^(3) = (11)/(2) m^(3) = 5.5 m^(3)` (ii) Let the reqiured height of water in the vessel be h metres Radius of the vessel, `r = (50)/(100)m = (1)/(2) m` Volume of water in the cylindrical vessel `= (pi r^(2)h) m^(3)` `= ((22)/(7) xx (1)/(2) xx (1)/(2) xx h) m^(3) = (11h)/(14) m^(3)` `:. (11h)/(14) = (11)/(2) rArr = ((11)/(2) xx (14)/(11)) m = 7m` Hence, the height of water in the cylindrical vessel is 7 m |
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| 7. |
There are 20 cylindrical pillars in a building, each having a diameter of 50 cm and height 4m. Find the cost of cleaning them at Rs 14 per `m^(2)`. |
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Answer» Correct Answer - Rs 1760 Lateral surface area to be cleared `= (2 xx (22)/(7) xx (25)/(100) xx 4 xx 20) m^(2) = ((880)/(7)) m^(3)` Cost of cleaning `= Rs ((880)/(7) xx 14) = Rs 1760` |
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| 8. |
Find the volume, the total surface area and the lateral surface area of a cuboid which is 15 m long, 12 m wide and 4.5 m high |
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Answer» Here, l = 15 m , b = 12 m and h = 4.5 m Volume of the cuboid `= (l xx b xx h)` cubic units `= (15 xx 12 xx 4.5) m^(3) = 810 m^(3)` Total surface area of the cuboid `= 2(lb + bh + lh)` sq units `= 2 (15 xx 12 + 12 xx 4.5 + 15 xx 4.5) m^(2) = 603 m^(2)` Lateral surface area of the cuboid `= [2 (l + b) xx h]` sq units `= [2(15 + 12) xx 4.5]m^(2) = 243 m^(2)` |
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| 9. |
Find the volume, the lateral surface area and the total surface area of the cuboid whose dimensions are: (i) length = 12 cm, breadth = 8 cm and height = 4.5 cm (ii) length = 26 m, breadth = 14 m and height = 6.5 m (iii) length = 15m, breadth = 6 m and height = 5 dm (iv) length = 24m, breadth = 25 cm and height = 6 m |
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Answer» Correct Answer - (i) `432 cm^(3), 180 cm^(2), 372 cm^(2)` (ii) `2366 m^(3), 520m^(2), 1248 m^(2)` (iii) `45 m^(3), 21 m^(2), 201 m^(2)` (iv) `36m^(3), 291 m^(2), 303 m^(2)` |
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| 10. |
The length, breadth and height of a cuboid are 15 cm, 12 cm and 4.5 cm respectively. Its volume isA. `243 cm^(3)`B. `405 cm^(3)`C. `810 cm^(3)`D. `603 cm^(3)` |
| Answer» Correct Answer - C | |
| 11. |
A rectangualr container whose base is a square of side 15 cm stands on a horizointal table and holds water up to 3cm from the top .When a cube is placed in the water and is completely submerged , the water rises to the top and 54 `cm^(3)` of water overflows. Calculate the volume of the cube and its surface area. |
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Answer» Correct Answer - 126800 `cm^(3)`,15880 `cm^(2)` Volume of the cube submerged = volume of water that fills 3cm height of the container +volume of water that overflows =`15xx15xx3+54=729 cm^(3)` If side of the cube submerged = x cm Its volume =`x^(3) cm^(3)` `x^(3)=729=9xx9xx9xx` x=9cm The side of the cube = 9cm And its surface area =`6xx(side^(2))=6xx9xx9=486 cm^(2)` |
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| 12. |
The volume of a cube is `512 cm^(3)`. Its total surface area isA. `256 cm^(2)`B. `384 cm^(2)`C. `512 cm^(2)`D. `64 cm^(2)` |
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Answer» Correct Answer - B `a^(3) = 512 = 8^(3) rArr a = 8cm` Total surface area `= 6a^(2) = (6 xx 8 xx 8) cm^(2) = = 384 cm^(2)` |
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| 13. |
If eachedge of a cube is increased by 50%, the percentage increase in its surfacearea is50% (b) 75%(c) 100% (d)125%A. 0.5B. 0.75C. 1D. 1.25 |
| Answer» Correct Answer - D | |
| 14. |
The sum oflength, breadth and depth of a cuboid is `19 c m`and lengthof its diagonal is `11 c mdot`Find thesurface area of the cuboid. |
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Answer» Correct Answer - `240 cm^(2)` `(l + b + h) = 19 cm and sqrt(l^(2) + b^(2) + h^(2)) = 11 cm` `rArr (l + b + h)^(2) = 361 cm^(2) and (l^(2) + b^(2) + h^(2)) = 212 cm^(2)` `rArr (l^(2) + b^(2) + h^(2)) + 2 (lb + bh + lh) = 361 cm^(2) and l^(2) + b^(2) + h^(2) = 121 cm^(2)` `rArr 212 cm^(2) + 2(lb + bh + lh) = 361 cm^(2)` `rArr 2(lb + bh + lh) = (361 - 121) cm^(2) = 240 cm^(2)` |
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| 15. |
The total surface area of a cube is `1176 cm^(2)`. Find its volume |
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Answer» Correct Answer - `2744 cm^(3)` `6a^(2) = 1176 rArr a^(2) = 196 = (14)^(2)` |
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| 16. |
In a shower, 5 cm of rain falls. Find the volume of water that falls on 2 heactares land |
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Answer» Correct Answer - `1000 m^(3)` Volume of water = (area `xx` depth) = `(2 xx 10000 xx (5)/(100)) m^(3)` |
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| 17. |
The length of the longest rod that can be placed in a room of dimensions `(10 m xx 10 m xx 5m)` is |
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Answer» Correct Answer - 15 m Length of the longest pole = length of diagonal `= sqrt(l^(2) + b^(2) + h^(2))` metres |
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| 18. |
The length of the longest rod that can fit in a cubical vessel of side 10 cm, isA. 10 cmB. 20 cmC. `10 sqrt2 cm`D. `10 sqrt3 cm` |
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Answer» Correct Answer - D Required length = length of its diagonal `= sqrt3a = (sqrt3 xx 10) cm = 10 sqrt3 cm` |
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| 19. |
A room is half as long again as it is broad. The cost of carpeting the room at Rs 13 per `m^(2)` is Rs 702 and the cost of papering the walls at Rs 7 per `m^(2)` is Rs 1204. If 1 door and 2 windown occupy `8 m^(2)`, find find dimensions of the room |
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Answer» Let the breadth of the room be x metres Then, its length `= (x + (x)/(2))` metres `= (3x)/(2)` metres Area of the floor `= (l xx b) = ((3x)/(2) xx x) m^(2) = (3x^(2))/(2) m^(2)` Also, area of the floor `= ("total cost of carpeting")/("rate per "m^(2))` `= ((702)/(13)) m^(2) = 54 m^(2)` `:. (3x^(2))/(2) = 54 rArr x^(2) = (54 xx (2)/(3)) = 36 = (6)^(2) rArr x = 6` `:.` breadth = 6m and length `= ((3)/(2) xx 6) m = 9m` Area of papered walls `= ("total cost of papering")/("rate per " m^(2))` `= (1204)/(7) m^(2) = 172 m^(2)` Area of 1 door and 2 windown `= 8 m^(2)` Area of 4 walls `= (172 + 8) m^(2) = 180 m^(2)` Let the height of the room be h metres Then, area of 4 walls `= {2 (l + b) xx h} = {2 (9 + 6) xxh} m^(2)` `= (30h) m^(2)` `:. 30h = 180 rArr h = (180)/(30) = 6m` Hence, length = 9m, breadth = 6m and height = 6m |
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| 20. |
The volume of a cube is `512 cm^(3)`. Its total surface area is |
| Answer» Correct Answer - `384 cm^(2)` | |
| 21. |
Three cubes of metal with edges 3cm, 4 cm and 5 cm respectively are melted to form a single cube. The lateral surface area of the new cube formed is |
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Answer» Correct Answer - `144 cm^(2)` Volume of the new cube `= (3^(3) + 4^(3) + 5^(3)) = cm^(3) = 216 cm^(3)` Edge of this cube = a cm, where `a^(3) = 216` `:.` a = 6 and the lateral surface area of the new cube is `4a^(2) cm^(2)` |
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| 22. |
Three cubes of metal whose edges are in the ratio 3:4:5 are melted down in to a single cube whose diagonal is `12(sqrt(3))` cm. Find the edges of the three cubes. |
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Answer» Correct Answer - 84 `pi cm^(2)`,12 `pi m^(3)` The ratio in the edges =3:4:5 Let edges be 3x,4xand 5x respectively. Volumes of three cubes will be `27x^(3),64x^(3)` and `125x^(3)`in `cm^(3)` respectively. Now sum of volumes of these three cubes `=27x^(2),64x^(3)`and `125 x^(3)`=`216x^(3)cm^(3)` Let edge of new cube be a cm. Diagonal of new cube=`asqrt(3)cm` `A(sqrt(3))=12(sqrt(12))` volume of new cube =`(12^(3))=1728 cm^(3)` Now by the given condition `216x^(3)=1728` `x^(3)=8` x=2 Edge of I cube =`3xx2=6cm` Edge of II =`4xx2=8 cm` Edge of III cube =5`xx`2=10 cm |
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| 23. |
If the length of diagonal of a cube is `8 sqrt3`cm then its surface area isA. `192 cm^(2)`B. `384 cm^(2)`C. `512 cm^(2)`D. `768 cm^(2)` |
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Answer» Correct Answer - B `sqrt3 a = 8 sqrt3 rArr a = 8 cm` `:.` its surface area `= 6a^(2) = (6 xx 8 xx 8) cm^(2) = 384 cm^(2)` |
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| 24. |
In a shower, 5 cm of rain falls. Find the volume of water that falls on 2 heactares landA. `500 m^(3)`B. `750 m^(3)`C. `800 m^(3)`D. `1000 m^(3)` |
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Answer» Correct Answer - D Required volume `= (2 xx 1000 xx (5)/(100)) m^(3) = 1000 m^(3)` |
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| 25. |
A river 1.5 m deep and 30 m wide is flowing at the rate of 3km per hour. The volume of water that rums into the sea per minute isA. `2000 m^(3)`B. `2250 m^(3)`C. `2500 m^(3)`D. `2750 m^(3)` |
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Answer» Correct Answer - B Volume of water running into the sea per hour `= ((3)/(2) xx 30 xx 3000) m^(3) = (45 xx 3000)m^(3)` Volume of water running into the sea per minute `= ((45 xx 3000))/(60) m^(3) = 2250 m^(3)` |
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| 26. |
The length of a cold storage is double itsbreadth. Its height is `3m e t r e sdot`The area of its four walls (including doors) is `108m^2dot`Find its volume. |
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Answer» Let the breadth of the cold storage be x metres Then, its length = 2x metres and height = 3 metres Area of the four walls of the cold storage `= {2 (l + b) xx h)` sq units `= {2 (2x + x) xx 3} m^(2) = (18x) m^(2)` But, area of 4 walls `= 108 m^(2)` (given) `:. 18x = 108 rArr x = (108)/(18) = 6` So, breadth = 6 m and length = 12 m Volume of the cold storage `= (l xx b xx h)` cubic units `= (12 xx 6 xx 3) m^(3) = 216 m^(3)` |
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| 27. |
The lateral surface area of a cube is `900 cm^(2)`. Find its volume |
| Answer» Correct Answer - `3375 cm^(3)` | |
| 28. |
Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9 m. (Take `sqrt3 = 1.73`) |
| Answer» Correct Answer - `729 m^(3), 324 m^(2), 486 m^(2), 15.57m` | |
| 29. |
Find the volume, total surface area, lateral surface area and the length of diagonal of a cube, each of whose edges measured 20 cm |
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Answer» Here, a = 20 cm Volume of the cube `= a^(3)` cubic units `= (20xx 20xx 20) cm^(3) = 8000 cm^(3)` Total surface area of the cube `= (6a^(2))` sq units `= (6 xx 20 xx 20) cm^(2) = 2400 cm^(2)` Lateral surface area of the cube `= (4a^(2))` sq units `= (4 xx 20 xx 20) cm^(2) = 1600 cm^(2)` Diagonal of the cube `= (sqrt3a)` units `= (sqrt3 xx 20) cm = (1.732 xx 20) cm` = 34.64 cm |
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| 30. |
Three cubes of metal with edges 3cm, 4 cm and 5 cm respectively are melted to form a single cube. The lateral surface area of the new cube formed isA. `72 cm^(2)`B. `144 cm^(2)`C. `128 cm^(2)`D. `256 cm^(2)` |
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Answer» Correct Answer - B Volume of new cube formed `= (3^(3) + 4^(3) + 5^(3)) cm^(3)` `= (27 + 64 + 125) cm^(3) = 216 cm^(3)` Let `a^(3) = 216 = 6^(3)`. Then, a = 6 cm Lateral surface area of the new cube `= 4a^(2) = (4 xx 6 xx 6) cm^(2) = 144 cm^(2)` |
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| 31. |
The lateral surface area of a cube is `256 m^(2)`. The volume of the cube isA. `64 m^(3)`B. `216 m^(3)`C. `256 m^(3)`D. `512 m^(3)` |
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Answer» Correct Answer - D `4a^(2) = 256 rArr a^(2) = 64 = 8^(2) rArr a = 8` `:.` volume `= a^(3) = (8 xx 8 xx 8)m^(3) = 512 m^(3)` |
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| 32. |
The lateral surface area of a cube is `324 cm^(2)`. Find its volume and the total surface area |
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Answer» Let each side of the cube be a cm then, the lateral surface area of the cube `= (4a^(2)) cm^(2)` `:. 4a^(2) = 324 rArr a^(2) = 81 rArr a = sqrt81 = 9` Volume of the cube `= a^(3) cm^(3)` `= (9 xx 9 xx 9) cm^(3) = 729 cm^(3)` Total surface area of the cube `= (6a^(2))` sq units `= (6 xx 9 xx 9) cm^(2) = 486 cm^(2)` |
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| 33. |
2.2 cubicdm of brass is to be drawn into a cylindrical wire 0.50 cm in diameter. Findthe length of the wire.A. 110 mB. 112 mC. 98 mD. 124 m |
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Answer» Correct Answer - B Volume of the wire `= (2.2 xx 10 xx 10 xx 10) cm^(3) = 2200 cm^(3)` Radius of the wire `= 0.25 cm = (25)/(100) cm = (1)/(4) cm` Let the length of wire be h cm. Then, `pi xx (1)/(4) xx (1)/(4) xx h = 2200 rArr (22)/(7) xx (1)/(16) xx h = 2200` `:. h = (2200 xx (7)/(22) xx 16) cm = ((11200)/(100)) m = 112 m` |
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| 34. |
The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii isA. `2 : 1`B. `4 : 1`C. `8 : 1`D. `1 : 1` |
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Answer» Correct Answer - B Let their slant heights be l and 2l and their radii be `R_(1) and R_(2)`. Then, `(piR_(1)l)/(pi R_(2)(2l)) = (2)/(1) rArr (R_(1))/(R_(2)) = (4)/(1) = 4 : 1` |
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| 35. |
The height of a cone is 24 cm and the diameter of its base is 14 cm. The curved surface area of the cone isA. `528 cm^(2)`B. `550 cm^(2)`C. `616 cm^(2)`D. `704 cm^(2)` |
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Answer» Correct Answer - B `l^(2) = (r^(2) + h^(2)) = 7^(2) + (24)^(2) = (49 + 576) = 625` `:. l = sqrt625 = 25 cm` Curved surface area `pi rl = ((22)/(7) xx 7 xx 25) cm^(2) = 550 cm^(2)` |
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| 36. |
The curved surface area of a cone is `308 cm^(2)` and its slant height is 14 cm. Find the radius of the base and total surface area of the cone. |
| Answer» Correct Answer - `7 cm, 462 cm^(2)` | |
| 37. |
The radius and the height of a right circular cone are in the ratio of `5 : 12` and its volume is 2512 cu cm. Find the curved surface area and the total surface area of the cone. (Use `pi = 3.14`) |
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Answer» Let radius = 5x cm and height = 12x cm. Then, volume `= [(1)/(3) xx 3.14 xx (5x)^(2) xx (12x)] cm^(3) = (314x^(3)) cm^(3)` `:. 314x^(3) = 2512 rArr x^(3) = ((2512)/(314)) = 8 rArr x = 2` `:.` radius = 10 cm and height = 24 cm `:.` slant height `= sqrt(r^(2) + h^(2)) = sqrt((10)^(2) + (24)^(2)) cm` `= sqrt(676) cm = 26 cm` So, area of the curved surface `= pir l` `= (3.14 xx 10 xx 26) cm^(2)` `816.4 cm^(2)` Total surface area = (curved surface area + base area) `= (816.4 + 3.14 xx 10 xx 10) cm^(2)` `= (816.4 + 314) cm^(2) = 1130.4 cm^(2)` |
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| 38. |
If h,C,V respecitively are the height the curved surface area and volume of a cone prove that `3piVh^(3)-C^(2)h^(2)+9V^(2)=0` |
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Answer» `C=pirl,V=(1)/(3)pir^(2)h, l^(2)=h^(2)+r^(2)` L.H.S=`3piVh^(3)-C^(2)h^(2)+9V^(2)` `=(3pi)((1)/(3)pir^(2)h)-(pirl)^(2)-(pirl)^(2)h^(2)+9((1)/(3)pir^(2)h)^(2)` `=pi^(2)r^(2)h^(4)-pi^(2)r^(2)h^(2)(h^(2)+r^(2))+9xx(1)/(9)pi^(2)r^(2)h^(2)` `pi^(2)r^(2)h^(4)-pi^(2)r^(2)h^(4)-pi^(2)r^(2)h^(4)-pi^(2)r^(4)h^(2)`=0=R.H.S |
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| 39. |
The volume of a right circular cone of height 24 cm is `1232 cm^(3)`. Its curved surface area isA. `1254 cm^(2)`B. `704 cm^(2)`C. `550 cm^(2)`D. `462 cm^(2)` |
| Answer» Correct Answer - C | |
| 40. |
If the height and the radius of a cone are doubled, the volume of the cone becomesA. 3 timesB. 4 timesC. 6 timesD. 8 times |
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Answer» Correct Answer - D Volume of a cone of height h and radius `r = (1)/(3) pi r^(2) h = V` New height = 2h and new radius = 2r `:.` new volume `= (1)/(3) pi (2r)^(2) xx 2h = 8 xx ((1)/(3) pi r^(2) h) = 8V` |
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| 41. |
A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to make n solid cones of height 1 cm and base radius 1 mm. The value of n isA. 450B. 1350C. 4500D. 13500 |
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Answer» Correct Answer - D n = number of cones `= ("volume of the cylinder")/("volume of 1 cone") = (pi xx 3 xx 3 xx 5)/((1)/(3)pi xx (1)/(10) xx (1)/(10) xx 1) = 13500` |
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| 42. |
Acylindrical container with diameter of base 56cm contains sufficient water tosubmerge a rectangular solid of iron with dimensions `32 c m x 22 c m x 14 c mdot`Find therise in the level of the water when the solid is completely submerged. |
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Answer» Correct Answer - 4 cm Let the rise in level be x cm. Then, volume of cylinder with base radius 28 cm and height x cm = volume of iron solid `:. (22)/(7) xx 28 xx 28 xx x = 32 xx 22 xx 14 rArr x = 4 cm` |
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| 43. |
Ata Ramzan Mela, a stall keeper in one of the food stalls has a largecylindrical vessel of base radius 15 cm filled up to a height of 32 cm withorange juice. The juice is filled in small cylindrical glasses (see Fig.13.27) of radius 3 cm u |
| Answer» Correct Answer - Rs 1500 | |
| 44. |
Find(i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is4.2 m in diameter and 4.5 m high.(ii) how much steel was actually used, if `1/(12)` of the steel actually used was wasted in making the tank |
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Answer» (i) Curved surface area =`2pirh=2xx(22)/(7)xx(4.2)/(2)xx4.5=5.9 m^(2)` (ii)Total steel used =Total surface area (Assuming thickness =0 m) `=2pir(r+h)` `=2xxx(22)/(7)xx(4.2)/(2)((4.2)/(2)+4.5)` `=(44)/(7)xx2.1xx(13.2)/(2)=22xx0.3xx13.2=87.12me^(2)` Let actural steel used is x `m^(2)` `(11)/(12)x=87.12` `x=(87.12xx12)/(11)=95.04 m^(2)` |
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| 45. |
The surface areas of two spheres are in the ratio `1 : 4`. Find the ratio of their volumes. |
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Answer» Correct Answer - `1 : 8` `(S_(1))/(S_(2)) = (1)/(4) rArr (4pi R_(1)^(2))/(4pi R_(2)^(2)) = (1)/(4) rArr (R_(1)^(2))/(R_(2)^(2)) = (1)/(4) rArr ((R_(1))/(R_(2)))^(2) = ((1)/(2))^(2) rArr (R_(1))/(R_(2)) = (1)/(2)` `(V_(1))/(V_(2)) = ((4)/(3) pi (R_(1)^(3)))/((4)/(2)pi (R_(2)^(3))) = (R_(1)^(3))/(R_(2)^(3)) = ((R_(1))/(R_(2)))^(3) = ((1)/(2))^(3) = (1)/(8) rArr V_(1) : V_(2) = 1 : 8` |
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| 46. |
The radii of two spheres are in the ratio `1 : 2`. Find the ratio of their surface areas. |
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Answer» Correct Answer - `1 : 4` Let the radii of the two spheres be x and 2x respectively. Then, `(S_(1))/(S_(2)) = (4pi x^(2))/(4pi (2x)^(2)) = (x^(2))/(4x^(2)) = (1)/(4) rArr S_(1) : S_(2) = 1 : 4` |
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| 47. |
The surface area of a sphere of radius 5 cm is five times the curved surface area of a cone of radius 4 cm. Find the height and volume (correct to two decimal places) of the cone. |
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Answer» Surface area of the given sphere `4pi R^(2) = (4pi xx 5 xx 5) cm^(2) = (100pi) cm^(2)` Radius of the base of the cone, r = 4 cm Let the slant height of the cone be `lcm`. Then, curved surface area of the given cone `= (pi rl) = (piu xx 4 xx l) cm^(2) = (4pil) cm^(2)` `:. 100pi = 5 xx (4pil) rArr l = 5 cm` Let the height of the cone h cm. Then, `l^(2) = h^(2) + r^(2) rArr h^(2) = (l^(2) - r^(2)) = (5^(2) - 4^(2)) = 9 rArr h = 3cm` Volume of the cone `= (1)/(3) pi r^(2)h` `=((1)/(3) xx 3.14 xx 4 xx 4 xx 3) cm^(3) = 50.24 cm^(3)` Hence, the height of the cone is 3 cm and its volume is `50.24 cm^(3)` |
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| 48. |
If the ratio of the volumes of two spheres is `1 : 8` then the ratio of their surface areas isA. `1 : 2`B. `1 : 4`C. `1 :8`D. `1 : 16` |
| Answer» Correct Answer - B | |
| 49. |
Find the volume, cuved surface area and the total surface area of a cone having base radius 35 cm and height 12 cm |
| Answer» Correct Answer - `15400 cm^(3), 4070 cm^(2), 7920 cm^(2)` | |
| 50. |
The volume of a sphere is `38808 cm^(3)`. Its curved surface area isA. `5544 cm^(2)`B. `8316 cm^(2)`C. `4158 cm^(2)`D. `1386 cm^(2)` |
| Answer» Correct Answer - A | |