Question

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

Answer 1

Radius of the heap, r = \(\frac{10.5}{2}\) m = 5.25 m
Height of the heap, h = 3 m

Volume of the heap = \(\frac{1}{3}\pi\)r²h

= \(\frac{1}{3}\) × \(\frac{22}{7}\) × 5.25 m × 5.25 m × 3 m
= 86.625 m³

Slant height,\(l = \sqrt{r² + h²}\)

\(= \sqrt{(5.25)² + (3)²}\)

\(= \sqrt{27.5625 + 9}\)

\(= \sqrt{36.5625}\)
= 6.046 m 

∴ The area of the canvas required to cover the heap = \(\pi\)rl
= \(\frac{22}{7}\) × 5.25 m × 6.046 m
= 99.825 m²
Therefore, 99.825 m² canvas will be provided to protect the heap from rain.