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 Rs 21 per litre.
(Use $\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Volume of container = $\frac{1}{3}\mathrm{\pi }h\left[R^2+Rr+r^2\right]$
$$\begin{gathered} =\frac{1}{3}\times \frac{22}{7}\times 24\left[{\left(20\right)}^2+20\times 8+8^2\right] \\ =\frac{22\times 8}{7}\times \left(400+160+64\right) \\ =\frac{22\times 8}{7}\times 624 \\ =15689.14{\mathrm{cm}}^3 \\ =\frac{15689.14}{1000}\mathit{}l\left[\because 1{\mathrm{cm}}^3=\frac{1}{1000}l\right] \\ \mathit{=}15.69\mathit{}l \end{gathered}$$
Cost of milk which can completely fill the container is given by
15.69 ⨯ 21
= Rs 329.49