# Radius of a Sphere

The radius of a sphere is the shortest distance from its center to any point on its surface. It is half the length of the diameter of the sphere. The radius, being a measure of length or distance is expressed in linear units such as mm, cm, m, in, or ft.

Shown below is the radius of a sphere.

## Formulas

There are four different ways to find the radius of a sphere based on the information given. Let us discuss each of them separately.

### With Surface Area

The equation to find the radius of a sphere with surface area is derived below.

As we know,

Surface Area (SA) = 4πr2, here π = 22/7 = 3.141, r = radius

=> r = √(SA/(4π))

Thus,

Radius (r) = √(SA/(4π))

Let us solve an example to illustrate the concept better.

Find the radius of a sphere with a surface area of 900 cm2.

Solution:

As we know,
Radius (r) = √(SA/(4π)),  here SA = 900 cm2, π = 22/7 = 3.141, r = radius
r = √(900 ÷ (4 × 3.141))
= 8.463 cm

### With Volume

The equation to find the radius of a sphere from volume is derived below.

As we know,

Volume (V) = (4/3)πr3, here π = 22/7 = 3.141, r = radius

=> r = (3V/4π)1/3

Thus,

Radius (r) = (3V/4π)1/3

Let us solve an example to illustrate the concept better.

Find the radius of a sphere with a volume of 523.6 cm3.

Solution:

As we know,
Radius (r) = (3V/4π)1/3, here π = 22/7 = 3.141, V = 523.6 cm3
r = (3 × 523.6 /4 × 3.141)1/3
= 5 cm

### With Diameter

As we know,

Diameter (d) = 2 × r, here r = radius

∴ r = d/2

Thus

Radius (r) = d/2, here d = diameter

Let us solve an example to illustrate the above concept better.

Find the radius of a sphere given the diameter of 12 cm.

Solution:

∴ r = d/2, here d = 12 cm
r = 12/2
= 6 cm

### With Circumference

As we know,

Circumference (C) = 2πr, here r = radius, π = 22/7 = 3.141

=> r = C/2π

Thus,

Radius (r) = C/2π

Let us solve an example to illustrate the above concept better.

Find the radius of a sphere with a circumference of 44 mm.

Solution:

As we know,
Radius (r) = C/2π, here C = 44 mm, π = 22/7 = 3.141
r = 44 /2 × 3.141
= 7.004 mm

Since the radius of a sphere is half the diameter, let us now find the diameter of a sphere given the volume.

Finding the diameter of a sphere when the VOLUME is known

Find the diameter of a sphere whose volume is 1436 mm3.

Solution:

Here we will use an alternative formula for the diameter of a sphere using the volume.
Diameter (d ) = ${\left( \dfrac{6V}{\pi }\right) ^{\dfrac{1}{3}}}$ , here V = 1436 mm3, π = 22/7 = 3.141
d = ${\left( \dfrac{6\times 1436}{3\cdot 141}\right) ^{\dfrac{1}{3}}}$
≈ 14 mm