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An open metal bucket is in the shape of a frustum of a cone of height 21 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at Rs. 30 per litre.

Text Solution

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Let R and r be the radii of the top and the base of the bucket respectively, and let h be its height.

Then, R = 20 cm, r = 10 and h = 21 cm.
Capacity of the bucket
= volume of frustum of the cone
`=1/3pih[R^(2)+r^(2)+Rr]`
`=[(1/3xx22/7xx21)""{(20)^(2)+(10)^(2)xx20xx10}]cm^(3)`
`(22xx700)cm^(3)=15400cm^(2)`.
Volume of milk that the bucket can hold.
`=((15400)/(1000))"litres"=15.4 " litres"`.
`:." cost of milk "= ₹(15.4xx30) = ₹ 462`.
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