20 + Interview Questions in PRISMS IN GENERAL AWARENESS Page 1 InterviewSolution

1.	The volume and base area of a square prism are 3600 cubic centimetre and 144 cm2 respectively. What is its total surface area ?
Answer» Volume of the prism = 3600 cm³ Base area × height = 3600 cm³ 144 × height = 3600 height = 3600/144 = 25 cm Surface area = Base area + Lateral surface area Lateral surface area = Base perimeter × height = 12 × 4 × 25 = 1200 cm² (Base area = 144, One side = √144 = 12 cm) Total surface area = 144 + 1200 = 1344 cm²

1.

The volume and base area of a square prism are 3600 cubic centimetre and 144 cm2 respectively. What is its total surface area ?

Answer»

Volume of the prism = 3600 cm³

Base area × height = 3600 cm³

144 × height = 3600

height = 3600/144 = 25 cm

Surface area = Base area + Lateral surface area

Lateral surface area = Base perimeter × height

= 12 × 4 × 25 = 1200 cm²

(Base area = 144, One side = √144 = 12 cm)

Total surface area = 144 + 1200 = 1344 cm²

Discussion

2.	A prism is made by cutting cardboard as shown in the figure.a. What is the name of the prism? b. What will be the area of the required cardboard for making the rectangle form?
Answer» a. Triangular prism b. Lateral area = base perimeter × height = (15 + 13 + 14) × 20 = 42 × 20 = 840 cm²

2.

A prism is made by cutting cardboard as shown in the figure.a. What is the name of the prism? b. What will be the area of the required cardboard for making the rectangle form?

Answer»

a. Triangular prism

b. Lateral area = base perimeter × height

= (15 + 13 + 14) × 20 = 42 × 20

= 840 cm²

Discussion

3.	The diameter of a water tank in the shape of a cylinder is 3 m and height 4 m. How many litres of water will the tank hold?
Answer» Radius = 1.5 m, Height = 4m Volume of the cylinder = Base area × height = πr²h = 3.14 × 1.5 × 1.5 × 4 = 28.26 m³ = 28.26 × 100 × 100 × 100 cm³ = 28260000 cm³ = 28260000/1000 = 28260 liter

3.

The diameter of a water tank in the shape of a cylinder is 3 m and height 4 m. How many litres of water will the tank hold?

Answer»

Radius = 1.5 m, Height = 4m

Volume of the cylinder

= Base area × height = πr²h = 3.14 × 1.5 × 1.5 × 4 = 28.26 m³

= 28.26 × 100 × 100 × 100 cm³

= 28260000 cm³ = 28260000/1000 = 28260 liter

Discussion

4.	Two tins in the shape of cylinder has radii 15 cm and 10 cm respectively. The heights are 25 cm and 18 cm respectively. In the both cylinders, the ghee are filled. When it transferred into another cylindrical-shaped tin. If there is ghee in the bigger tin with height 30 cm. Then find its radius.
Answer» ‘Volume of the ghee in the first tin = πr² h = π × 15 × 15 × 25 = 5625π cm³ Volume of the ghee in the second tin = πr² h = π × 10 × 10 × 18 = 1800 π cm³ Total volume = 5625 π + 1800 π = 7425 π cm³ Volume of the ghee in the bigger tin = πr² h = 7425 π h = 30 πr²h = πr² × 30 = 7425 π r²= \(\frac{7425\pi}{30\pi}\) = 247.5 \(r=\sqrt{247.5}=15.73\) cm

4.

Two tins in the shape of cylinder has radii 15 cm and 10 cm respectively. The heights are 25 cm and 18 cm respectively. In the both cylinders, the ghee are filled. When it transferred into another cylindrical-shaped tin. If there is ghee in the bigger tin with height 30 cm. Then find its radius.

Answer»

‘Volume of the ghee in the first tin

= πr² h = π × 15 × 15 × 25 = 5625π cm³

Volume of the ghee in the second tin

= πr² h = π × 10 × 10 × 18 = 1800 π cm³

Total volume = 5625 π + 1800 π

= 7425 π cm³ Volume of the ghee in the bigger tin

= πr² h = 7425 π

h = 30

πr²h = πr² × 30 = 7425 π

r²= \(\frac{7425\pi}{30\pi}\) = 247.5

\(r=\sqrt{247.5}=15.73\) cm

Discussion

5.	The diameter of a road roller is 80 centimetres and it is 1.20 metres long:What is the area of levelled surface, when it rolls once?
Answer» Radius of roller = 40 cm Length of roller (height) = 1.20 m = 120 cm Area of leveled surface, when it rolls once = Curved surface area of the roller = 2 × π × Radius × Height = 2 × 3.14 × 40 × 120 = 30144 cm² = 3.0144 m²

5.

The diameter of a road roller is 80 centimetres and it is 1.20 metres long:What is the area of levelled surface, when it rolls once?

Answer»

Radius of roller = 40 cm

Length of roller (height) = 1.20 m = 120 cm

Area of leveled surface, when it rolls once

= Curved surface area of the roller

= 2 × π × Radius × Height

= 2 × 3.14 × 40 × 120 = 30144 cm² = 3.0144 m²

Discussion

6.	If the base length, width, height of a quadrangular prism are 37.5 cm, 18 cm, 40 cm respectively. Find the area of cube which has same volume as that of this prism.
Answer» Volume of quadrangular prism = base area × height = 37.5 × 18× 40 = 27000 cm³ Volume of quadrangular prism = Volume of cube ∴ Volume of cube = 27000 cm³ Let one side of a cube be x, then a³ = 27000 ; a = 30 cm 30 × 30 × 30 = 27000, Hence Surface area of the cube = 6a² = 6 × 30 × 30 = 5400 cm²

6.

If the base length, width, height of a quadrangular prism are 37.5 cm, 18 cm, 40 cm respectively. Find the area of cube which has same volume as that of this prism.

Answer»

Volume of quadrangular prism = base area × height = 37.5 × 18× 40 = 27000 cm³

Volume of quadrangular prism = Volume of cube

∴ Volume of cube = 27000 cm³

Let one side of a cube be x, then a³ = 27000

; a = 30 cm

30 × 30 × 30 = 27000, Hence

Surface area of the cube = 6a² = 6 × 30 × 30

= 5400 cm²

Discussion

7.	If a wooden piece is in the shape of square prism has base 12 cm and height 70 cm. What is the maximum volume of the cylinder that can be carved out of it?
Answer» Diameter of the largest cylinder = 12cm Radius = 6 cm, Height = 70 cm Volume of the cylinder = base area × height = πr² h = π × 6 × 6 × 70 = 7912.8 cm³

7.

If a wooden piece is in the shape of square prism has base 12 cm and height 70 cm. What is the maximum volume of the cylinder that can be carved out of it?

Answer»

Diameter of the largest cylinder = 12cm

Radius = 6 cm, Height = 70 cm

Volume of the cylinder

= base area × height

= πr² h = π × 6 × 6 × 70 = 7912.8 cm³

Discussion

8.	A tin with length 40 cm width 20 cm and height 20 cm, which is in the shape of a quadrangular prism has sugar-filled in it. If the sugar is measured using a cylindrical vessel with radius 4 cm and height 15 cm, then how many times can the sugar be measured using the vessel?
Answer» Volume of the quadrangular prism = 50 × 40 × 20 Volume of the cylinder = πr²h. = 3.14 × 4 × 4 × 15 Number of times the sugar can be measured = \(\frac{50\times40\times20}{3.14\times4\times4\times15}\) = 53 times

8.

A tin with length 40 cm width 20 cm and height 20 cm, which is in the shape of a quadrangular prism has sugar-filled in it. If the sugar is measured using a cylindrical vessel with radius 4 cm and height 15 cm, then how many times can the sugar be measured using the vessel?

Answer»

Volume of the quadrangular prism = 50 × 40 × 20

Volume of the cylinder = πr²h.

= 3.14 × 4 × 4 × 15

Number of times the sugar can be measured = \(\frac{50\times40\times20}{3.14\times4\times4\times15}\) = 53 times

Discussion

9.	The base area and the curved surface area of a cylinder are equal. What is the ratio of the base radius and height?
Answer» Curved surface area of the cylinder = Base perimeter x height = 2 πrh Base perimeter = πr² If it is equal, 2 π rh = πr² 2rh = r × r, 2h = r i.e., The radius is twice the height.

9.

The base area and the curved surface area of a cylinder are equal. What is the ratio of the base radius and height?

Answer»

Curved surface area of the cylinder = Base

perimeter x height = 2 πrh

Base perimeter = πr²

If it is equal, 2 π rh = πr²

2rh = r × r, 2h = r

i.e., The radius is twice the height.

Discussion

10.	A cylinder has base radius 4 cm and height 10 cm. Then find its lateral surface area.
Answer» Perimeter of a circle with radius 4 cm = 2 × π × 4 = 8π cm. Curved surface area of the cylinder = Base perimeter × height = 8 π × 10 = 80 π cm²

10.

A cylinder has base radius 4 cm and height 10 cm. Then find its lateral surface area.

Answer»

Perimeter of a circle with radius 4 cm = 2 × π × 4 = 8π cm.

Curved surface area of the cylinder = Base

perimeter × height = 8 π × 10 = 80 π cm²

Discussion

11.	A cylinder has height 20 cm and base radius 4 cm. Then find its volume.
Answer» When the square of the radius is multiplied by π we get the area of the circle. Base area of the cylinder = π × 4² = 16 π cm² The height of the cylinder is 20 cm Volume = 16 π × 20 = 320 π cm³

11.

A cylinder has height 20 cm and base radius 4 cm. Then find its volume.

Answer»

When the square of the radius is multiplied by π we get the area of the circle.

Base area of the cylinder

= π × 4² = 16 π cm²

The height of the cylinder is 20 cm

Volume = 16 π × 20 = 320 π cm³

Discussion

12.	Two identical prisms with right triangles as base are joined to form a rectangular prism as shown below:What is total surface area?
Answer» The sides of the rectangular prism are Length = 12 cm Breadth = 5 cm and Height = 15 cm. Base area = 2 × perimeter of rectangle 2 × 12 × 5 = 120 cm² Lateral surface area = base perimeter × height = 2 (length + breadth) × height = 2(12 + 5) × 15 = 2 × 17 × 15 = 510 cm² Total surface area = 120 + 510 = 630 cm²

12.

Two identical prisms with right triangles as base are joined to form a rectangular prism as shown below:What is total surface area?

Answer»

The sides of the rectangular prism are

Length = 12 cm

Breadth = 5 cm and

Height = 15 cm.

Base area = 2 × perimeter of rectangle

2 × 12 × 5 = 120 cm²

Lateral surface area = base perimeter × height

= 2 (length + breadth) × height = 2(12 + 5) × 15

= 2 × 17 × 15 = 510 cm²

Total surface area = 120 + 510 = 630 cm²

Discussion

13.	The base radius of an iron cylinder is 15 centimetres and its height is 32 centimetres. It is melted and re-cast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?
Answer» Volume of the first cylinder = π R² H = π (15)² x 32 = 7200 π Volume of the melted and recast cylinder = π r²h = π (20)² x h = 400 π h Volume remains constant when melted. 400 π h = 7200π h = \(\frac{7200\pi}{400\pi}\) = 18 Height of the second cylinder = 18 cm

13.

The base radius of an iron cylinder is 15 centimetres and its height is 32 centimetres. It is melted and re-cast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?

Answer»

Volume of the first cylinder

= π R² H = π (15)² x 32 = 7200 π

Volume of the melted and recast cylinder = π r²h = π (20)² x h = 400 π h

Volume remains constant when melted.

400 π h = 7200π

h = \(\frac{7200\pi}{400\pi}\) = 18

Height of the second cylinder = 18 cm

Discussion

14.	A hollow prism of base a square of side 16 centimetres contains water 10 centimetres high. If a solid cube of side 8 centimetres is immersed in it, by how much would the water level rise?
Answer» When a solid cube is immersed into water, the volume of water is raised. Sum of the volume of the water at first time and volume of the solid cube immersed equally to the product of base area and height of water level now. Volume of the water at first = Base area × height = 16 × 16 × 10 = 2560 cm³ Volume of the solid cube when edges are 8 cm = 8 × 8 × 8 = 512 cm³ Height at first = 10 cm Water level raised = 12 -10 = 2 cm

14.

A hollow prism of base a square of side 16 centimetres contains water 10 centimetres high. If a solid cube of side 8 centimetres is immersed in it, by how much would the water level rise?

Answer»

When a solid cube is immersed into water,

the volume of water is raised.

Sum of the volume of the water at first time and volume of the solid cube immersed equally to the product of base area and height of water level now.

Volume of the water at first = Base area × height

= 16 × 16 × 10 = 2560 cm³

Volume of the solid cube when edges are 8 cm

= 8 × 8 × 8 = 512 cm³

Height at first = 10 cm

Water level raised = 12 -10 = 2 cm

Discussion

15.	The base of a prism is an equilateral triangle of perimeter 12 centimetres and its height is 5 centimetres. What is its total surface area?
Answer» Base perimeter of equilateral triangular prism = 12 cm Base side = 12/3 = 4 cm Lateral surface area of equilateral triangular prism = Base perimeter × Height = 12 × 5 = 60 cm² Base area of equilateral triangular prism = \(\frac{\sqrt{3}}{4}\times4^2\) = 4√3 = 6.92 cm² Total surface area of equilateral triangular prism = 60 + 2 × 6.92 = 73.84 cm²

15.

The base of a prism is an equilateral triangle of perimeter 12 centimetres and its height is 5 centimetres. What is its total surface area?

Answer»

Base perimeter of equilateral triangular

prism = 12 cm

Base side = 12/3 = 4 cm

Lateral surface area of equilateral triangular prism = Base perimeter × Height

= 12 × 5 = 60 cm²

Base area of equilateral triangular prism = \(\frac{\sqrt{3}}{4}\times4^2\) = 4√3 = 6.92 cm²

Total surface area of equilateral triangular

prism = 60 + 2 × 6.92 = 73.84 cm²

Discussion

16.	The base edge of a square prism is 15 cm.The total surface area is 1950 m2.i. What is its height ?ii. Calculate the volume.
Answer» i. Base edge = 15 cm Total surface area = Base area + Lateral surface area = 2a² + 4ah (base egde is ‘a’) 1950 = 2 × 15² + 4 × 15 × h 1950 = 450 + 60h 60h = 1950 – 450 = 1500 h = 1500/60 = 25 cm ii. Volume = a² × h = 15 × 15 × 25 = 5625 cm³

16.

The base edge of a square prism is 15 cm.The total surface area is 1950 m2.i. What is its height ?ii. Calculate the volume.

Answer»

i. Base edge = 15 cm

Total surface area = Base area + Lateral surface area

= 2a² + 4ah (base egde is ‘a’)

1950 = 2 × 15² + 4 × 15 × h

1950 = 450 + 60h

60h = 1950 – 450 = 1500

h = 1500/60 = 25 cm

ii. Volume = a² × h = 15 × 15 × 25

= 5625 cm³

Discussion

17.	If a box in the shape of a square prism has length 25 cm, 20 cm width and 7-litre volume. What will be its height?
Answer» Volume = 7 litre = 7000 cm³ lbh = 7000 25 × 20 × h = 7000 h = \(\frac{7000}{25\times20}\) = 14 cm

17.

If a box in the shape of a square prism has length 25 cm, 20 cm width and 7-litre volume. What will be its height?

Answer»

Volume = 7 litre = 7000 cm³

lbh = 7000

25 × 20 × h = 7000

h = \(\frac{7000}{25\times20}\) = 14 cm

Discussion

18.	The diameters of two-cylinder are in the ratio 2 : 3 and their heights in the ratio 5: 4. If the volume of the first cylinder is 400 cm , then find the volume of the second cylinder.
Answer» The diameters of two-cylinder are in the ratio 2 : 3 so the radius of the cylinders are also 2:3. Assume that radius of first cylinder is 2r and second cylinder be 3r. Assume that height of first cylinder is 5h and second cylinder be 4h. Volume of the first cylinder = πr²h = π × 2r × 2r × 5h = 20 πr² Volume of the second cylinder = πr²h = π × 3r × 3r × 4h = 36 πr² h Ratio between volumes = 20πr² h : 36πr² h = 20 : 36 = 5 : 9 Volume of the first cylinder is 400. If the volume of second cylinder be x, then 5 : 9 = 400: x; 5x = 400 × 9 x = \(\frac{400\times9}{5}\) = 80 × 9 = 720 cm³

18.

The diameters of two-cylinder are in the ratio 2 : 3 and their heights in the ratio 5: 4. If the volume of the first cylinder is 400 cm , then find the volume of the second cylinder.

Answer»

The diameters of two-cylinder are in the ratio 2 : 3 so the radius of the cylinders are also 2:3.

Assume that radius of first cylinder is 2r and second cylinder be 3r.

Assume that height of first cylinder is 5h and second cylinder be 4h.

Volume of the first cylinder = πr²h

= π × 2r × 2r × 5h = 20 πr²

Volume of the second cylinder = πr²h

= π × 3r × 3r × 4h = 36 πr² h

Ratio between volumes

= 20πr² h : 36πr² h = 20 : 36 = 5 : 9

Volume of the first cylinder is 400.

If the volume of second cylinder be x, then

5 : 9 = 400: x; 5x = 400 × 9

x = \(\frac{400\times9}{5}\) = 80 × 9 = 720 cm³

Discussion

19.	The base radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:4.i. What is the ratio of their volumes?ii. The volume of the first cylinder is 720 cubic centimetres. What is the volume of the second?
Answer» i. If the base radius of the first cylinder is 2r then base radius of the second one is 3r. Height of the first cylinder is 5h and second cylinder is 4h. Volume of the first cylinder = Base area × height . = π × 2r × 2r × 5h = 20 π r²h. Volume of the second cylinder = π × 3r × 3r × 4h = 36 πr²h. The ratio between the volumes = 20πr² h : 36πr² h = 20 : 36.= 5 : 9 ii. The volume of the first cylinder is 720 cm³ is given. Let consider the volume of the second cylinder be x, then the ratio between the volumes is 5: 9 5 : 9 = 720 : x 5 × x = 9 × 720 x = 1296 Volume of the second cylinder = 1296 cm³

19.

The base radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:4.i. What is the ratio of their volumes?ii. The volume of the first cylinder is 720 cubic centimetres. What is the volume of the second?

Answer»

i. If the base radius of the first cylinder is 2r then base radius of the second one is 3r. Height of the first cylinder is 5h and second cylinder is 4h.

Volume of the first cylinder

= Base area × height .

= π × 2r × 2r × 5h = 20 π r²h.

Volume of the second cylinder

= π × 3r × 3r × 4h = 36 πr²h.

The ratio between the volumes

= 20πr² h : 36πr² h = 20 : 36.= 5 : 9

ii. The volume of the first cylinder is 720 cm³ is given. Let consider the volume of the second cylinder be x, then the ratio between the volumes is 5: 9

5 : 9 = 720 : x

5 × x = 9 × 720

x = 1296

Volume of the second cylinder = 1296 cm³

Discussion

20.	A cylinder made of metal has radius 18 cm and height 40 cm. When this melts how many cylinders can be made of radius 2 cm and height 5 cm?
Answer» Volume of the first cylinder = π r² H = π (18)² × 40 = 12960 π cm³ Volume of the newly made cylinder = π (2)² × 5 = 20π cm³ Number of the new fly made cylinders = \(\frac{12360\pi}{20\pi}\) = 648 cylindres

20.

A cylinder made of metal has radius 18 cm and height 40 cm. When this melts how many cylinders can be made of radius 2 cm and height 5 cm?

Answer»

Volume of the first cylinder = π r² H = π

(18)² × 40 = 12960 π cm³

Volume of the newly made cylinder = π (2)² × 5 = 20π cm³

Number of the new fly made cylinders

= \(\frac{12360\pi}{20\pi}\) = 648 cylindres

Discussion

Explore topic-wise InterviewSolutions in .

The volume and base area of a square prism are 3600 cubic centimetre and 144 cm2 respectively. What is its total surface area ?

A prism is made by cutting cardboard as shown in the figure.a. What is the name of the prism? b. What will be the area of the required cardboard for making the rectangle form?

The diameter of a water tank in the shape of a cylinder is 3 m and height 4 m. How many litres of water will the tank hold?

Two tins in the shape of cylinder has radii 15 cm and 10 cm respectively. The heights are 25 cm and 18 cm respectively. In the both cylinders, the ghee are filled. When it transferred into another cylindrical-shaped tin. If there is ghee in the bigger tin with height 30 cm. Then find its radius.

The diameter of a road roller is 80 centimetres and it is 1.20 metres long:What is the area of levelled surface, when it rolls once?

If the base length, width, height of a quadrangular prism are 37.5 cm, 18 cm, 40 cm respectively. Find the area of cube which has same volume as that of this prism.

If a wooden piece is in the shape of square prism has base 12 cm and height 70 cm. What is the maximum volume of the cylinder that can be carved out of it?

A tin with length 40 cm width 20 cm and height 20 cm, which is in the shape of a quadrangular prism has sugar-filled in it. If the sugar is measured using a cylindrical vessel with radius 4 cm and height 15 cm, then how many times can the sugar be measured using the vessel?

The base area and the curved surface area of a cylinder are equal. What is the ratio of the base radius and height?

A cylinder has base radius 4 cm and height 10 cm. Then find its lateral surface area.

A cylinder has height 20 cm and base radius 4 cm. Then find its volume.

Two identical prisms with right triangles as base are joined to form a rectangular prism as shown below:What is total surface area?

The base radius of an iron cylinder is 15 centimetres and its height is 32 centimetres. It is melted and re-cast into a cylinder of base radius 20 centimetres. What is the height of this cylinder?

A hollow prism of base a square of side 16 centimetres contains water 10 centimetres high. If a solid cube of side 8 centimetres is immersed in it, by how much would the water level rise?

The base of a prism is an equilateral triangle of perimeter 12 centimetres and its height is 5 centimetres. What is its total surface area?

The base edge of a square prism is 15 cm.The total surface area is 1950 m2.i. What is its height ?ii. Calculate the volume.

If a box in the shape of a square prism has length 25 cm, 20 cm width and 7-litre volume. What will be its height?

The diameters of two-cylinder are in the ratio 2 : 3 and their heights in the ratio 5: 4. If the volume of the first cylinder is 400 cm , then find the volume of the second cylinder.

The base radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:4.i. What is the ratio of their volumes?ii. The volume of the first cylinder is 720 cubic centimetres. What is the volume of the second?

A cylinder made of metal has radius 18 cm and height 40 cm. When this melts how many cylinders can be made of radius 2 cm and height 5 cm?