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 π = 3.14.)

Answer 1

It is given that

Diameter of the conical heap = 9m

Radius of the conical heap = 9/2 = 4.5m

Height of the conical heap = 3.5m

We know that

Volume of the conical heap = 1/3 πr²h

By substituting the values

Volume of the conical heap = 1/3 × 3.14 × 4.5² × 3.5

On further calculation

Volume of the conical heap = 3.14 × 1.5 × 4.5 × 3.5

So we get

Volume of the conical heap = 74.1825 m³

We know that

Slant height l =√ (r² + h²)

By substituting the values

l = √ (4.5² + 3.5²)

On further calculation

l = √ 32.5

So we get

l = 5.7 m

We know that

Curved surface area of the conical heap = πrl

By substituting the values

Curved surface area of the conical heap = 3.14 × 4.5 × 5.7

On further calculation

Curved surface area of the conical heap = 80.54 m²

Therefore, 80.54 m² of canvas is required to cover the heap of wheat.