A heap of wheat is in the form of a cone of diameter 16.8 m and height 3.5 m. Find its volume. How much cloth is required to just cover the heap?

Given,

Diameter of heap of cone = 16.8 m

Radius of heap of cone (r) = $\dfrac{16.8}{2}$ = 8.4 m

Height (h) = 3.5 m

Volume of cone = $\dfrac{1}{3}πr^2h$

$= \dfrac{1}{3} \times \dfrac{22}{7} \times (8.4)^2 \times 3.5 \\[1em] = \dfrac{22}{21} \times 246.96 \\[1em] = \dfrac{5433.12}{21} \\[1em] = 258.72 \text{ m}^3.$

We know that,

⇒ l² = r² + h²

⇒ l² = (8.4)² + (3.5)²

⇒ l² = 70.56 + 12.25

⇒ l² = 82.81

⇒ l = $\sqrt{82.81}$ = 9.1 cm.

Cloth required to cover the heap = Curved surface area of heap = πrl

= $\dfrac{22}{7} \times 8.4 \times 9.1$

= 240.24 m².

Hence, volume = 258.72 m³ and cloth required to cover the heap = 240.24 m².