# ACT Math : How to find the radius of a sphere

## Example Questions

### Example Question #1 : How To Find The Radius Of A Sphere

The surface area of a sphere is  feet. What is the radius?

Explanation:

Solve the equaiton for the surface area of a sphere for the radius and plug in the values:

### Example Question #2 : Spheres

What is the radius of a sphere with a volume of  ?  Round to the nearest hundredth.

Explanation:

Recall that the equation for the volume of a sphere is:

For our data, we know:

Solve for . First, multiply both sides by :

Now, divide out the :

Using your calculator, you can solve for . Remember, if need be, you can raise  to the power of  if your calculator does not have a variable-root button.

This gives you:

If you get something like , just round up. This is a rounding issue with some calculators.

### Example Question #3 : How To Find The Radius Of A Sphere

The volume of a sphere is . What is the diameter of the sphere? Round to the nearest hundredth.

Explanation:

Recall that the equation for the volume of a sphere is:

For our data, we know:

Solve for . Begin by dividing out the  from both sides:

Next, multiply both sides by :

Using your calculator, solve for . Recall that you can always use the  power if you don't have a variable-root button.

You should get:

If you get , just round up to . This is a general rounding problem with calculators. Since you are looking for the diameter, you must double this to .

### Example Question #4 : How To Find The Radius Of A Sphere

What is the radius of a sphere with a surface area of  ?  Round to the nearest hundredth.

Explanation:

Recall that the surface area of a sphere is found by the equation:

For our data, this means:

Solve for . First, divide by :

Take the square root of both sides:

### Example Question #5 : How To Find The Radius Of A Sphere

What is the radius of a sphere with a volume of ?

Explanation:

Given the volume of the sphere, , you need to use the formula for volume of a sphere  and work backwards to find the radius. I would multiply both sides by  to get rid of the  in the formula. You then have . Next, divide both sides by  so that all vyou have left is . Finally take the cube root of , to get  units for the radius.

### Example Question #6 : How To Find The Radius Of A Sphere

A cube with sides of  is circumscribed by a sphere, such that all eight vertices of the cube are tangent to the sphere. What is the sphere's radius?