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) = 4πr^{2}, 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 cm^{2}.

Solution:

As we know, Radius (r) = √(SA/(4π)), here SA = 900 cm^{2}, 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)πr^{3}, 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 cm^{3}.

Solution:

As we know, Radius (r) = (3V/4π)^{1/3}, here π = 22/7 = 3.141, V = 523.6 cm^{3} ∴ 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 mm^{3}.

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 mm^{3}, π = 22/7 = 3.141 ∴ d = ${\left( \dfrac{6\times 1436}{3\cdot 141}\right) ^{\dfrac{1}{3}}}$ ≈ 14 mm