Question

if in a sphere, volume and surface area are numerically equal, then find its radius​

Answer 1

Answer:

Radius of the sphere is 3 units.

Explanation:

Given that volume and surface area of a square are numerically equal.

Let the radius of the sphere = r

Surface area of a sphere = 4πr²

Volume of a sphere = 4/3πr³

According to the question:

Surface area = Volume

⟹ 4πr² = 4/3πr³

⟹ 4 × π × r × r × = 4/3 × π × r × r × r

⟹ 4 = 4/3r

⟹ 4 × 3/4 = r

⟹ 12/4 = r

⟹ 3 = r

Radius is 3 units

More:

• Sphere is a three dimensional ( 3-D) shape.
• A sphere has all points of its boundary equidistant from a common point called its centre.
• The equal distance is called the radius of the sphere.
• The extent of the sphere is called the diameter of the sphere. 2(radius) = diameter

Answer 2

Answer:

Radius of the sphere is 3 units.

Let the radius of the sphere = r

Surface area of a sphere = 4πr²

Volume of a sphere = 4/3πr³

According to the question:

Surface area = Volume

$\bold{⟹ 4πr² = 4/3πr³}$

$\bold{⟹ 4 × π × r × r × = 4/3 × π × r × r × r}$

$\bold{⟹ 4 = 4/3r}$

$\bold{⟹ 4 × 3/4 = r}$

$\bold{⟹ 12/4 = r}$

$\bold{⟹ 3 = r}$

Radius is 3 units

hope it helps you