If a sphere has the same surface area as the total surface area of a circular cone of height 40 cm and radius 30 cm, find the radius of the sphere.

Question

Philoid · Accepted Answer

Let the radius of the sphere be r cm.

Given –

Height of cone(h) = 40 cm

Radius of cone(r) = 30 cm

∴ Slant height of cone(l) = √(h² + r²) = √(40² + 30²) = 50 cm

According to question –

Surface Area of Sphere = Total Surface Area of Circular Cone

⇒ 4 × π × r² = π × r × (r + l)

⇒ 4r = r + l

⇒ 3r = l

∴ r = (l/3) = (50/3) cm

Thus, the radius of the Sphere = (50/3) cm