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Question 12
A milk container of height 16 cm is made of metal sheet in the form of a 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.

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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
=πh3(R2+r2+Rr)=227×163[(20)2+(8)2+20×8]=22×1621(400+64+160)=22×16×62421=21964821=10459.42 cm3=10.45942 L[1L=1000 cm3]
So, volume of the milk container is 10459 . 42 cm3
Cost 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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