Question

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 ₹44 per litre which the container can hold. 

Answer 1

Radius, r₁ = 8 cm and r₂ = 20 cm
Height, h = 16 cm
Volume of milk that the container can hold

\[V = \frac{1}{3}\pi h\left( r_1^2 + r_1 r_2 + r_2^2 \right)\]

\[V = \frac{1}{3}\pi \times 16\left( 8^2 + 8 \times 20 + {20}^2 \right)\]

\[V = 10459 . 42 {cm}^3 = 10 . 45942 \text { liters }\]

Cost of milk will be \[10 . 45942 \times 44 = \text { Rs }460 . 21\]