Question

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

Answer 1

It is given that

Diameter of the conical heap $=9m$

Radius of the conical heap $=\frac{9}{2}=4.5m$

Height of the conical heap $=3.5m$

We know that

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

By substituting the values

Volume of the conical heap $=\frac{1}{3}\times 3.14\times {4.5}^2\times 3.5$

On further calculation

Volume of the conical heap $=3.14\times 1.5\times 4.5\times 3.5$

So we get

Volume of the conical heap $=74.1825m^3$

We know that

Slant height $l=\sqrt{(r^2+h^2)}$

By substituting the values

$l=\sqrt{({4.5}^2+{3.5}^2)}$

On further calculation

$l=\sqrt{32.5}$

So we get

$l=5.7m$

We know that

Curved surface area of the conical heap $=\pi rl$

By substituting the values

Curved surface area of the conical heap $=3.14\times 4.5\times 5.7$

On further calculation

Curved surface area of the conical heap $=80.54m^2$

Therefore, $80.54m^2$ of canvas is required to cover the heap of wheat.