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Surface Area and Volume of a Sphere

The surface area of a sphere is the number of square units that will exactly cover its surface.

surface area and volume of a sphere

The formula for the surface area of a sphere is given by:

A = 4r²?

where A represents the area and r represents the radius.

If you already know the surface area and need to find the radius, we can rearrange the above formula and solve it for r:


and now take the square root of both sides:

divide both sides with 4?

The volume of a sphere is the number of cubic units that will exactly fill the sphere.

Volume of a sphere is given by:


where V represents the volume and r is the radius.

Again, we can solve the above formula for r and thus find the radius if we are given the volume:



and now take the third root of both sides


divide both sides with

Interesting fact

The shape with the smallest possible surface area for a given volume is a sphere. Or in other words, the sphere is a shape with the largest volume for a fixed surface area.

The sphere therefore appears in nature in water drops, bubbles, planets etc.

Example I

Find the surface area and the volume of a sphere with radius 5.

To do this, simply plug in r=5 into the formulas.

For the area:

We can plug in 3.14? for and get:

For the volume:

Again, we can plug in 3.14 for ? and get:

Example II

Find the radius of a sphere with a volume of 65.42.

Now we’ll use the last formula provided above, the one solved for r. Plug in 65.42 for V and 3.14 for ?:

More Examples

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