Mensuration

6 )

What is the volume of a cylinder whose curved surface area is 1408 cm² and height is 16 cm?

7715 cm3

9340 cm3

8722 cm3

7346 cm3

9856 cm3

View Solution

Answer :

2nrh = 1408, h = 16

Solve both, so r = 14

Volume = n r²h = (22/7) * 14 * 14 * 16 =

9856

7 )

A cone with diameter of its base as 30 cm is formed by melting a spherical ball of diameter 10 cm. What is the approximate height of the cone?

6 cm

3 cm

2 cm

5 cm

None of these

View Solution

Answer :

Radius of cone = 30/2 = 15,

radius of ball = 10/2 = 5

Volumes will be equal,

so (1/3) n r²h = (4/3) n R³15²h = 4* 5³

So h = 2.2

8 )

A cylinder whose base of circumference is 6 m can roll at a rate of 3 rounds per second. How much distance will the cylinder cover in 9 seconds?

125 m

162 m

149 m

173 m

157m

View Solution

Answer :

Distance covered in one round = 2 x n x r ^:6 m

Distance covered in 1 second = 3 x 6 = 18 m

So distance covered in 9 seconds = 18⁹= 162m

9 )

A container is formed by surmounting a hemisphere on a right circular cylinder of same radius as that of hemisphere. If the volume of the container is 576n m³ and radius of cylinder is 6 m, then find the height of the container.

14 m

12 m

20 m

18 m

22 m

View Solution

Answer :

Volume of the container = Volume of the cylinder + Volume of the hemisphere Volume of the container = n 6^{1 2}h + (2/3) n 6³ = 576n

= n 36 (h + 4) = 576n

Solving we get h = 12

So the height of the container = 12 + 6 = 18 m

10 )

The radii of two cylinders are in the ratio 3 : 2 and their curved surface areas are in the ratio 3 : 5. What is the ratio of their volumes?

8 : 11

5 : 9

7 : 4

9 : 10

13 : 7

View Solution

Answer :

r1/r2 = 3/2 or r1 = 3/2 * r2 CSA1/CSA2 = 2nr1h1/2nr2h2 = 3/5 So h1/h2 = 2/5

Volumel/ Volume2 = nr1²h1/ nr2²h2 = 9/10

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