Question

THE SURFACE AREA OF A SPHERE OF RADIUS 5CM IS 5 TIME THE CURVED SURFACE AREA OF A CONE OF RADIUS 4CM FIND THE VOLUME OF THE CONE

Answer 1

Let R be the radius of the sphere.

Suppose the radius of cone be r and h respectively.

Surface area of the sphere = 4πR2 = 4π (5 cm)2 = 100π cm2

Curved surface area of cone = πrl = π × 4 cm × l = 4πl

Given, Surface area of the sphere = 5 × Curved surface area of the cone

∴ 100π cm2 = 5 × 4π l cm

⇒ 100π cm2 = 20πl cm

⇒ l = 5 cm

Slant height of the cone, √r²+h²

∴ (4 cm)2 + h 2 = (5 cm)2

⇒ h 2 = 25 cm2 – 16 cm2

⇒ h 2 = 9 cm2

⇒ h = 3 cm

Height of the cone, h = 3 cm

∴ Volume of the cone =1/3πr²h
=1/3×22/7×4×4×3

=352/7cm²

Answer 2

i think its probably right