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Question
A milk container of height 16 cm is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.
Solution
Given that, height of milk container (h) = 16 cm,
Radius of lower end of milk container (r) = 8 cm
And radius of upper end of milk container (R) = 20 cm
∴ Volume of the milk container made of metal sheet in the form of a frustum of a cone
= `(πh)/3 (R^2 + r^2 + Rr)`
= `22/7 xx 16/3 [(20)^2 + (8)^2 + 20 xx 8]`
= `(22 xx 16)/21 (400 + 64 + 160)`
= `(22 xx 16 xx 624)/21`
= `219648/21`
= 10459.42 cm3 ......[∵ 1L = 1000 cm3]
= 10.45942 L
So, volume of the milk container is 10459.42 cm3
∵ Cost of 1 L milk = ₹ 22
∴ Cost of 10.45942 L milk = 22 × 10.45942 = ₹ 230.12
Hence, the required cost of milk is ₹ 230.12
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