A heap of wheat is in the form of a cone whose diameter is $ 10.5 \mathrm{~m} $ and height is $ 3 \mathrm{~m} $. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

 Given:

A heap of wheat is in the form of a cone whose diameter is \( 10.5 \mathrm{~m} \) and height is \( 3 \mathrm{~m} \).

To do:

We have to find its volume and the canvas cloth required to cover the heap.

Solution:

Diameter of the conical heap of wheat $= 10.5\ m$

This implies,

Radius $(r)=\frac{10.5}{2} \mathrm{~m}$

$=5.25 \mathrm{~m}$

Height of the conical heap $(h)=3 \mathrm{~m}$

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

$=\frac{1}{3} \times \frac{22}{7} \times 5.25 \times 5.25 \times 3$

$=86.625 \mathrm{~m}^{3}$

We know that,

$l^2=r^2+h^2$

$\Rightarrow l=\sqrt{r^{2}+h^{2}}$

$=\sqrt{(5.25)^{2}+(3)^2}$

$=\sqrt{27.5625+9}$

$=\sqrt{36.5625}$

$=6.05$

Curved surface area of the heap $=\pi r l$

$=\frac{22}{7} \times 5.25 \times 6.05$

$=99.825 \mathrm{~cm}^{2}$

 The area of the canvas required is $99.825 \mathrm{~cm}^{2}$.