# Intermediate Geometry : How to find the radius of a sphere

## Example Questions

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

If the volume of a sphere is , what is the approximate length of its diameter?

Explanation:

The correct answer is 6.12 ft.

Plug the value of  into the equation so that

Multiply both sides by 3 to get

Then divide both sides by  to get

Then take the 3rd root of both sides to get 3.06 ft for the radius.  Finally, you have to multiply by 2 on both sides to get the diameter. Thus

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

The volume of a sphere is . What is its radius?

Explanation:

The formula for the volume of a sphere is:

The only given information in the problem is the sphere's final volume. If the volume is , the formula for volume can be used to calculate the sphere's radius.

In this case, , the radius, is the only unknown variable that needs to be solved for.

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

The area of a sphere is . What is its radius?

Explanation:

The only information given is the area of

This problem may be approached "backwards," where the area formula for a sphere can be used to solve for the radius. This is possible because the formula for area is  , where  (the radius) is what we're looking for. After  is substituted in for the area, the goal is to solve for  by getting it by itself on one side of the equals sign.

### Example Question #2 : How To Find The Radius Of A Sphere

If the volume of a sphere is , what is the sphere's exact radius?

Explanation:

Write the formula for the volume of a sphere:

Plug in the given volume and solve for the radius, .

Start by multiplying each side of the equation by :

Now, divide each side of the equation by :

Finally, take the cubed root of each side of the equation:

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

Given the volume of a sphere is , what is the radius?

Explanation:

The equation for the volume of a sphere is:

, where  is the length of the sphere's radius.

Plug in the given volume and solve for  to calculate the sphere's radius:

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

If the volume of a sphere is , what is the radius of the sphere?

Explanation:

The formula for the volume of a sphere is:

, where  is the sphere's radius.

Plug in the volume and solve for , the sphere's radius:

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

Find the radius of a sphere if the surface area is .

Explanation:

The formula for the surface area of a sphere is:

Substitute the given value for the sphere's surface area into the equation and solve for  to find the radius:

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

Find the radius of a sphere if its surface area is .