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.
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