# A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m.

Question:

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use π = 3.14).

Solution:

Radius of the heap, $r=\frac{9}{2} \mathrm{~m}=4.5 \mathrm{~m}$

Height of the heap, h = 3.5 m

$\therefore$ Volume of the heap of wheat $=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times 3.14 \times(4.5)^{2} \times 3.5=74.1825 \mathrm{~m}^{3}$

Now,

Slant height of the heap, $l=\sqrt{r^{2}+h^{2}}=\sqrt{(4.5)^{2}+(3.5)^{2}}=\sqrt{20.25+12.25}=\sqrt{32.5} \approx 5.7 \mathrm{~m}$

∴ Area of the canvas cloth required to just cover the heap of wheat

= Curved surface area of the heap of wheat

$=\pi r l$

$\approx 3.14 \times 4.5 \times 5.7$

$\approx 80.541 \mathrm{~m}^{2}$

Thus, the area of canvas cloth required to just cover the heap is approximately 80.541 m.