Question

A semi-circular lamina of radius 35 cm is folded so that the two bounding radii are joined together to form a cone. Find:

1. the radius of the cone.
2. the lateral surface area of the cone.

Answer 1

Given

Radius of the semicircle

R = 35 cm 

When the lamina is folded into a cone:

The arc length of the semicircle becomes the circumference of the base of the cone

The radius of the semicircle becomes the slant height of the cone

(i) Radius of the cone:

Arc length of a semicircle:

= πR = π × 35 = 35π

Let r be the radius of the cone.

Circumference of the cone’s base:

2πr

Equating:

2πr = 35π

`r = 35/2`

= 17.5 cm

Radius of the cone = 17.5 cm

(ii) Lateral surface area of the cone

Slant height: l = 35 cm

Lateral surface area of a cone: πrl

Substitute values:

π × 17.5 × 35

Using π = `22/7`

`22/7 × 17.5 × 35`

= 1925 cm²