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Q.

What will be the height of a bucket, which is in the form of a frustum of a cone that can hold 28.49 litres of water and the radii of its circular ends are 28 cm and 21 cm?

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a

25 cm

b

15 cm

c

20 cm

d

40 cm

answer is B.

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Detailed Solution

We have to find the height of the bucket, which is in the form of a frustum of a cone that can hold 28.49 litres of water and the radii of its circular ends are 28 cm and 21 cm.
1 L=1000 cm3
Suppose, the height of the bucket=h.
Note that,
Volume of the bucket=28.49 L
=28.490 cm3
Using the formula,
Volume of the frustum,
=

13 π h (R 2 + r 2)

Where, R= radius of upper base and r= radius of lower base

⇒ 13 × 227 × h × (282 + 212 + 28 × 21) = 28490 ⇒ h = 28490 × 3 22 × 7 × 37

⇒ h = 15 c m

So, the height of the bucket is 15cm.
Therefore, option 2 is correct.

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