Question

Question 6
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Answer 1

Given that, a heap of rice is in the form of a cone.
Height of a heap of rice i.e cone (h) = 3.5 m
And diameter of a heap of rice i.e , cone = 9 m
Radius of a heap of rice i.e , cone $\left(r\right)=\frac{9}{2}m$
So, Volume of rice $=\frac{1}{3}\pi \times r^{2}h=\frac{1}{3}\times \frac{22}{7}\times \frac{9}{2}\times \frac{9}{2}\times 3.5=\frac{6237}{84}=74.25m^3$
Now , canvas cloth required to just cover heap of rice
= Surface area of a heap rice
$=\pi rl=\frac{22}{7}\times r\times \sqrt{r^2+h^2}=\frac{22}{7}\times \frac{9}{2}\times \sqrt{{\left(\frac{9}{2}\right)}^2+(3.5{)}^2}=\frac{11\times 9}{7}\times \sqrt{\frac{81}{4}+12.25}$
= $\frac{99}{7}\times \sqrt{\frac{130}{4}}$
= $14.142\times 5.7=80.61m^2$
Hence, $80.61m^2$ canvas cloth is required to just cover the heap.