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.
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
