Question

A metal container, open from the top, is in the shape of a frustum of a cone of height 21 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 35 per litre.\[\left[ Use \pi = \frac{22}{7} \right]\]

Answer 1

Given:
Height of the metal container, h = 21 cm
Radius of the lower end of the metal container, r = 8 cm
Radius of the upper end of the metal container, R = 20 cm

Volume of the metal container =\[\frac{1}{3}\pi h\left[ R^2 + Rr + r^2 \right]\]

\[= \frac{1}{3} \times \frac{22}{7} \times 21 \times \left[ \left( 20 \right)^2 + 20 \times 8 + 8^2 \right]\]
\[ = \frac{1}{3} \times \frac{22}{7} \times 21 \times 624\]
\[ = 13728 {cm}^3\]

\[= \frac{13728}{1000} L \left[ \because 1 L = 1, 000 {cm}^3 \right]\]
\[ = 13 . 728 L\]

Now,

Cost of 1 L of milk = Rs 35

∴ Cost of 13.728 L of milk = Rs 35 × 13.728 = Rs 480.48
 
Hence, the cost of the milk that can completely fill the container at the rate of Rs 35 per litre is Rs 480.48.