# A heap of rice is in the form of a cone of diameter 9 m

Question:

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

heap?

Solution:

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 $i . \theta .$, cone $(r)=\frac{9}{2} \mathrm{~m}$

So, volume of rice $=\frac{1}{3} \pi \times r^{2} h$

$=\frac{1}{3} \times \frac{22}{7} \times \frac{9}{2} \times \frac{9}{2} \times 3.5$

$=\frac{6237}{84}=74.25 \mathrm{~m}^{3}$

Now, canvas cloth required to just cover heap of rice

$=$ Surface area of a heap of rice

$=\pi /$

$=\frac{22}{7} \times r \times \sqrt{r^{2}+h^{2}}$

$=\frac{22}{7} \times \frac{9}{2} \times \sqrt{\left(\frac{9}{2}\right)^{2}+(3.5)^{2}}$

$=\frac{11 \times 9}{7} \times \sqrt{\frac{81}{4}+12.25}$

$=\frac{99}{7} \times \sqrt{\frac{130}{4}}=\frac{99}{7} \times \sqrt{32.5}$

$=14.142 \times 5.7$

$=80.61 \mathrm{~m}^{2}$

Hence, 80.61 m2 canvas cloth is required to just cover heap.