Question

A circular sheet of radius 18 centimetre is divided into
9 equal sectors. [3]
(a) Find the measure of the central angle of a sector.
(b) Find the slant height of a cone which can be made
by a sector.
(c) Find the lateral surface area of the cone thus
formed.

Answer 1

Step-by-step explanation:

a circular sheet of radius 18 cm is divided into 9 equal sectors

(a) central angle of a sector , θ = 360°/number of divisions of circular sheet

= 360°/9 = 40°

(b) slant height of cone which can be made by a sector, l = radius of circular sheet = 18cm

(c) radius of cone = r

we know, θ = l/r

⇒40° × π/180° = 2πR/r

⇒2π/9 = 2π × 18cm/r

⇒r = 2cm

hence, radius of cone is 2cm.

now lateral surface area of cone = πrl

= 22/7 × 2 × 18cm

= 792/7

= 113.14 cm²