Explore topic-wise InterviewSolutions in .

Correct option is (b) 19404 cm^3

The explanation: We know that CURVED surface area of a hemisphere is equal to 2πr^2.

2πr^2 = 2772

R^2 = \(\frac{2772*7}{2*22}\) = 441

Therefore, r = 21cm

Now, we know that volume of a hemisphere is equal to \(\frac{2}{3}\) πr^3.

Hence, V = \(\frac{2}{3}\) πr^3

= \(\frac{2*22*21*21*21}{3*7}\)

= 19404 cm^3.

The correct answer is (d) \(\FRAC{2}{3} πr^3\)

For EXPLANATION: Volume of a hemisphere is half the volume of a SPHERE.

We know that volume of a sphere of radius r is equal to \(\frac{4}{3} πr^3\).

Therefore, volume of a hemisphere is equal to \(\frac{2}{3} πr^3\).

Correct option is (a) 2310cm^3

Explanation: We KNOW that VOLUME of a cone = \(\frac{1}{3}\) πr^2h

= \(\frac{1}{3} * \frac{22}{7}\) * 21 * 21 * 5

= 6930cm^3.

Correct choice is (a) 40 seconds

For EXPLANATION: VOLUME of the container = 20 * 10 * 10

= 2000cm^3

Time REQUIRED to fill the container = \(\FRAC{Volume \,of \,container}{Flow \,rate \,of \,water}\)

= 2000/50

= 40 seconds.

The correct option is (B) L^3

Easy explanation: VOLUME of a cube of SIDES equal to l is GIVEN by l^3.

Right answer is (c) ₹420

To elaborate: For the tank, l = 2M, B = 3m and h = 1.5m (given).

The total area of the tank = 2{(2*3) + (3*1.5) + (2*1.5)}

= 2{13.5}

= 27 m^2

But it is given that all sides except the base are to be painted.

Hence, total area to be painted = 27 – (2*3)

= 21 m^2

Now, the cost of painting 1 m^2 = ₹20

Hence, the cost of painting 21 m^2 = 21 * 20 = ₹420.

The CORRECT answer is (b) 264

The BEST I can explain: Outer radius ro = 4cm

Inner radius ri = outer radius – thickness

= 4 – 3

ri = 1cm

This means that the sphere is hollow and volume of metal required = \(\frac{4}{3} πr_o^3 – \frac{4}{3} πr_i^3\)

= \(\frac{4}{3} π (4^3 – 1^3)\)

= \(\frac{4*22*63}{3*7}\)

= 264 cm^3.

Correct option is (B) \(\frac{1}{3}\)

The explanation: We know that VOLUME of a CONE = \(\frac{1}{3}\) πr^2h and volume of a cylinder= πr^2h

Hence, \(\frac{volume \,of \,a \,cone}{volume \,of \,a \,cylinder} = \frac{1/3 πr^2 h}{πr^2 h}\)

= \(\frac{1}{3}\).

The CORRECT option is (b) ₹14500

Explanation: The total area to be plastered = curved surface area + base area

= 2πrh + πr^2

= \((2 * \frac{22}{7} * 1.75 * 8) + {\frac{22}{7}*(8)^2}\)

= 88 + 201.14

= 289.14 m^2

≈ 290 m^2

The cost of PLASTERING area of 1 m^2 = ₹50

Therefore, the cost of plastering area of 290 m^2 = 290 * 50

= ₹14500.

The CORRECT ANSWER is (a) l * b * H

The explanation: VOLUME of a cuboid of length l, BREADTH b and height h = l * b * h

The correct choice is (B) 4πr^2

The BEST explanation: If a sphere has RADIUS equal to ”r”, then its SURFACE AREA is given by 4πr^2.

Correct choice is (a) 2πrh + 2πr^2

For EXPLANATION I WOULD say: Total surface AREA of a cylinder = curved surface area + 2 * area of the circular base

If we unfold the cylinder given in the above FIGURE, the area of the rectangle gives US the area of curved surface area of a cylinder (As shown in the figure below).

One side of the rectangle is equal to “h” and the other side is equal to perimeter of circular edge of the cylinder, i.e. “2πr”.

Hence, the curved surface area of the cylinder = 2πr * h

= 2πrhArea of circular base = 2πr^2

Hence, total surface area of a cylinder = curved surface area + 2 * area of the circular base

= 2πrh + 2πr^2.

The correct answer is (c) 2:1

Explanation: It can be SEEN that h = 4r … (1)

We know that curved surface AREA of a cylinder = 2πrh

And surface area of a sphere = 4πr^2

(We know that curved surface area of a cylinder)/(And surface area of a sphere) = 2πrh/(4πr^2)

= \(\FRAC{2πr(4r)}{4πr^2}\) (From RESULT (1))

= \(\frac{2πrh}{4πr^2}\)

= 2/1.

The correct choice is (B) 5

Explanation: Volume of a cylindrical glass = πr^2h

= \(\frac{22}{7}\) * 3.5 * 3.5 * 8

= 308cm^3

Volume of a water jug = 1540cm^3

Therefore, number of TIMES the water has to be POURED from glass to fill the jug COMPLETELY

= \(\frac{Volume \,of \,a \,water \,jug}{Volume \,of \,a \,cylindrical \,glass} = \frac{1540}{308}\)

= 5.

Correct choice is (C) πr^2h

Easiest explanation: Volume of a cylinder can be given by multiplying base area with its HEIGHT.

Hence, volume of a cylinder having RADIUS r and height H is equal to πr^2h where πr^2 is base area and h is height.

The correct answer is (d) 840

Easy EXPLANATION: For wall, length = 3m = 300cm, BREADTH = 12cm and height = 7M = 700cm

Volume of the wall = 300 * 12 * 700

= 2520000cm^3

Volume of bricks = 25 * 12 * 10

= 3000cm^3

Number of bricks REQUIRED = \(\frac{Volume \,of \,the \,wall}{Volume \,of \,one \,brick}\)

= 252000/3000

= 840.

The CORRECT option is (b) ₹7200

To explain I would say: Total surface area of the cubical tank = 6l^2

= 6(1.8)^2

= 19.44 m^2

= 194400 cm^2

It is given that tiles are to be covered leaving the base.

Hence, the total area that is to be covered by tiles = 19.44 – (1.8*1.8)

= 16.2 m^2

= 162000 cm^2

Area of ONE TILE = 30*30 = 900 cm^2

Hence, total number of tiles required = \(\frac{Total \,area \,that \,is \,to \,be \,covered \,by \,tiles}{Area \,of \,one \,tile}\)

= \(\frac{162000}{900}\)

= 180

180 tiles = \(\frac{180}{12}\) = 15 dozens of tiles

Total cost of tiles = RATE of tiles/dozen * Total number of dozens tiles required

= 400*18

= ₹7200.

Correct OPTION is (d) 30CM

Easy explanation: We know that the curved surface area of a CONE = πrl

πrl = 1980

\(\frac{22}{7}\) * 21 * l = 1980

l = 30cm.

Right choice is (a) 63.25 kg

The best I can explain: LET the OUTER radius = ro = 3cm

Inner radius = ri = 2cm

Height (here length) = l = 5M = 500cm

Volume of PIPE = π * (ro ^2 – ri ^2) * l

= \(\frac{22}{7}\) * (3^2 – 2^2) * 500

= 7857.14cm^3

Mass of 1cm^3 is 8.05 gram

Therefore, mass of 7857.14cm^3 is equal to 8.05 * 7857.14

= 63249.97gm

≈ 63250 gm

= 63.25 kg.

Correct answer is (a) ₹140800

To explain: The CURVED surface are of a conical tent = πrl

= \(\FRAC{22}{7}\) * 28 * 20

= 1760m^2

Cost of 1m^2 of material = ₹80

Hence, the total cost of 1760m^2 = 1760 * 80

= ₹140800.

Right option is (b) 704 cm^2

The best I can explain: Given, R = 7CM and H = 24cm

From the figure,

We can SAY that according to the Pythagoras theorem, l^2 = r^2 + h^2

= 7^2 + 24^2

= 625

Therefore, l = 25cm

We know that total surface area of a cone = πrl + πr^2

= πr (l + r)

= \(\frac{22}{7}\) * 7 (25+7)

= 704 cm^2.

Correct choice is (b) 2(LB + bh + lh)

Explanation: As shown in the figure below,

The total surface area of a cuboid is the sum of the area of six RECTANGLES CONSTITUTING the cuboid.

The six rectangles forms three pairs of rectangles (which are at opposite sides) who have the same surface area.

Area of one pair of rectangles having sides l and b = 2(l*b)

Area of the second pair of rectangle having sides b and h = 2(b*h)

Area of the THIRD pair of rectangle having sides l and h = 2(l*h)

The total area of the cuboid = sum of three pairs of rectangles

= 2(l*b) + 2(b*h) + 2(l*h)

= 2(lb + bh + lh).

Right CHOICE is (C) \(\frac{1}{3}\) πr^2h

Easiest explanation: Volume of three cones is equal to volume of a cylinder which has the same radius and HEIGHT as the cone.

We know that volume of a cylinder = πr^2h

Hence, volume of a cone = \(\frac{1}{3}\) πr^2h.

Right answer is (d) 231cm^3

The BEST explanation: We KNOW that base area of a CYLINDER is equal to πr^2.

Volume of a cylinder = πr^2h

= 21 * 11

= 231cm^3.

Correct option is (C) 14CM

The BEST I can explain: We know that the volume of a cuboid = L * b * h

12 * 7 * h = 1176

h = 14cm.

Correct OPTION is (d) 42

For explanation I would say: We KNOW that total surface AREA of a hemisphere = 3πr^2

3πr^2= 4158

3 * \(\FRAC{22}{7}\) * r^2 = 4158

r^2 = 441

Hence, r = 21cm

Therefore, diameter of hemisphere = 2r = 2 * 21 = 42cm.

The correct choice is (b) False

For explanation I WOULD say: For the cone to be RIGHT circular cone, the line joining its vertex to the CENTRE of its base have to be perpendicular to the base. (As shown in the below figure)

But we can see in the given figure that the line is not perpendicular to the base, HENCE the given cone is not right circular cone.

Correct answer is (a) 10cm

The BEST I can explain: Volume of a cylinder having radius r and height H is equal to πr^2h.

πr^2h = 1540

\(\FRAC{22}{7}\) * 7 * 7 * h = 1540

h = 10cm.

Right answer is (d) 26.7m^2

To explain I would say: The area of material required will be EQUAL to total SURFACE area of the cylinder.

We know that the total surface area of the cylinder = 2πrh + 2πr^2

= \((2 * \frac{22}{7} * 0.56 * 1.8) + {2 * \frac{22}{7} * (1.80)^2}\)

= 6.336 + 20.365

= 26.7 m^2.

The correct option is (b) 28

The explanation: The effective area that will be in contact with the pitch is the curved surface area of the cylinder.

Diameter of the ROLLER = 0.7m

Hence, RADIUS of the roller = 0.35m and height (length here) of the roller = 1m

We know that curved surface area of a cylinder = 2πr

= 2 * \(\frac{22}{7}\) * 0.35 * 1

= 2.2 m^2

Area of the cricket pitch = 60m^2

Let’s assume that the roller MAKES “n” revolutions to move once over the pitch.

Therefore, n * curved surface area of the roller = surface area of the pitch

n = \(\frac{Surface \,area \,of \,the \,pitch}{Curved \,surface \,area \,of \,the \,roller}\)

= \(\frac{60}{2.2}\)

= 27.27

≈ 28 revolutions.

The correct option is (d) 4cm

The best I can explain: Volume of a cylinder having radius r and height h is equal to πr^2h.

πr^2h = 176

\(\frac{22}{7}\) * 14 * r^2 = 176

r^2 = 4

Therefore, r = 2cm

We KNOW that DIAMETER = 2 * radius

= 2 * 2

= 4cm.

The correct option is (a) 6

For explanation I would say: For the box, l = 25, B = 30 and h = 45 (given)

TOTAL SURFACE area of the box = 2(lb + bh + LH)

= 2{(25*30) + (30*45) + (25*45)}

= 2{3225}

= 6450 cm^2.

1075 cm^2 of area can be painted by one container.

Therefore, to paint 6450 cm^2 of area, number of containers requires are = \(\frac{6450}{1075}\) = 6.

Correct CHOICE is (d) 15 days

Easiest EXPLANATION: Requirement of water of village for one day = 1500 * 200

= 300000 litres

= \(\frac{300000}{1000}\) m^3

= 300m^3

Volume of the water container = 15 * 25 * 12

= 4500m^3

Number of days for which the water in the container WOULD last = \(\frac{Volume \,of \,the \,container}{Water \,requirement \,of \,village \,for \,one \,day} = \frac{4500}{300}\)

= 15 days.

The correct option is (c) ₹1760

For explanation: We KNOW that CURVED surface area of We know that the curved surface area of a CONE = πrl

For the given conical vessel, r = 14cm and L = 20cm (given)

Hence, curved surface area of vessel = πrl

= \(\frac{22}{7}\) * 14 * 20

= 880cm^2

Now, the cost of painting 1cm^2 area = ₹2

Then the cost of painting 880cm^2 area = 880*2

= ₹1760.

The CORRECT choice is (d) 30cm

To EXPLAIN I would say: We KNOW that curved surface area of a cylinder = 2πrh

Curved surface area = 2640 cm^2 and r = 14 cm (given)

Therefore, 2 * \(\FRAC{22}{7}\) * 14 * h = 2640

h = 30cm.

Right answer is (d) \(\frac{1}{9}\)

The explanation: Let the radius of the balloon before PUMPING the air be “R”, then

A1 = 4πr^2

The radius of the balloon after pumping the air = 3r (given)

HENCE, A2 = 4π(3r)^2

Therefore, \(\frac{A_1}{A_2} = \frac{4πr^2}{4π(3r)^2} = \frac{1}{9}\).

Right CHOICE is (d) 6l^2

To elaborate: A cube has six equal SIDES.

Hence, total surface area of a cube = sum of AREAS of 6 sides (as shown in the FIGURE below)

Area of one SIDE of a cube having side equal to ‘l’ = l^2

Total surface area of the cube = l^2 + l^2 + l^2+l^2+ l^2 + l^2

= 6l^2.

The CORRECT ANSWER is (b) 1/√2

Easy explanation: We know that SURFACE area of a sphere of radius “R” is GIVEN by 4πR^2 and

curved surface area of hemisphere of radius “r” is EQUAL to 2πr^2.

It is given that surface area of a sphere of radius “R” is equal to curved surface area of a hemisphere of radius “r”.

Hence, 4πR^2 = 2πr^2

2R^2 = r^2

\(\frac{R^2}{r^2} = \frac{1}{2}\)

\(\frac{R}{r} = \frac{1}{\sqrt{2}}\).

Correct answer is (c) 2πrh

For explanation: If we unfold the cylinder GIVEN in the above figure, the area of the rectangle gives us the area of CURVED surface area of a cylinder (As shown in the figure below).

One side of the rectangle is EQUAL to “h” and the other side is equal to perimeter of circular edge of the cylinder, i.e. “2πr”.

HENCE, the curved surface area of the cylinder = 2πr * h

= 2πrh.