A container, open the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 24 per litre.
Given: height of frustum container = h = 24 cm
Radius of lower circular end = r = 8 cm
Radius of upper circular end = R = 20 cm
Cost of 1 litre milk = 24 Rs
Volume of milk completely fill the container = volume of frustum of cone
= 8 × 3.14 × (400 + 64 + 160) cm3
= 8 × 3.14 × 624 cm3
= 15674.88 cm3
Now, 1 litre is 1000 cm3
∴ 15674.88 cm3 = 15674.88/1000 = 15.67488 litres
∴ Cost of milk which can completely fill the container = 15.67488 × cost of 1 litre milk
= 15.67488 × 24 Rs
= 376.19712 Rs
∴ Cost of milk which can completely fill the container = 376.19712 Rs