Question

A container open at 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 21 per litre. [use π=22/7]

Answer 1

Solution:
Volume of a frustum of a cone ${\displaystyle =\frac{1}{3}\pi h(r{1}^2+r{2}^2+r1\times r2)}$

Volume of container ${\displaystyle =\frac{1}{3}\pi h(R^2+r{2}^2+Rr)}$

${\displaystyle =\frac{1}{3}\times \frac{22}{7}\times 24[20\times 20+8\times 8+20\times 8]}$

${\displaystyle =15689.14c{m}^3}$

${\displaystyle =15.69litre}$

The cost of milk which can completely fill the container at the rate of Rs.21 per liter =Rs(21 x 15.69) = 329.49