Question

A heap of rice is in the form of a cone with a diameter of 9m and a height of 3.5m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Answer 1

Volume of cone = $\frac{1}{3}$ $\pi r^2{h}^{}$

D = 9 m , r = $\frac{9}{2}$ m

Volume = $\frac{1}{3}$ $\times$ $\frac{22}{7}$ $\times$ $\frac{9}{2}$$\times$ $\frac{9}{2}$$\times$ (3.5) = 74.25 $m^3$

Just to cover the heap, we need the CSA of the cone.

Slant height of cone = sqrt{$r^2+h^2$} = sqrt{ [ $\frac{9}{2}$ $\times$ $\frac{9}{2}$ + (3.5)$\times$ (3.5) ] = 5.7008 m

CSA= $\pi rl$ = $\frac{22}{7}$ $\times$ $\frac{9}{2}$ $\times$ (5.7008) = 80.6256 m

Hence, the volume of rice is 74.25 $m^3$ and canvas cloth required to just cover the heap is 80.6256 m