Question

Two cones are made using two sectors of central angles 60° and 120° of a circle. If the radius of the smaller cone is 5cm

a. Calculate the radius and base area of the smaller cone.

b. Find the surface area of the bigger cone.

Answer 1

a. Central angle of the small sector = 60°

\(\frac{1}{6}\) part of the area of the circle Base radius of cone formed from above sector = 5 cm

Radius of the circle = 5 × 6 = 30

Similarly, area of the sector of central angle 120° = \(\frac{1}{3}\) of the area of the circle Base radius of the bigger cone = \(30\times\frac{1}{3}\) = 10

Base area of the bigger cone = π × 102 = 100 ×

b. Curved surface area ofthe bigger cone = π × 10 × 30 = 300π

Surface area = 100π + 300π = 400π cm²