Question

A cone of height 24cm and its base radius 6cm, a reshapes it into a sphere. Find radius of

sphere.​

Answer 1

Radius of sphere is 6cm.

Explanation :-

Given that, A reshapes cone with sphere.

▶.°. Volume of cone = Volume of sphere

▶ Height(h) of cone = 24cm

▶ Base Radius (r) = 6cm

As we know that,

Volume of cone = 1/3 πr²h.

▶Volume of cone = 1/3 × π × (6)² × 24

▶ Volume of cone = 1/3 × π × 36 × 24

▶ Volume of cone = π × 12 × 24

▶ Volume of cone = 288π

Now, we know that,

▶ Volume of sphere = 4/3 πr³.

▶ Volume of sphere = 4/3 πr³

Given that, Volume of cone = Volume of sphere

▶ 288π = 4/3 πr³

▶r³ = 288π × 3 /4π

▶r³ = 72 × 3

▶r³ = 216

▶r³ = (2 × 2 × 2 × 3 × 3 × 3)

▶r³ = 2^1/3 × 3^1/3

▶r = (2^3)^1/3 × (3^3)^1/3

▶r = 2 × 3

▶r = 6cm

Hence,

• The radius of sphere is 6cm.