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

## Example Questions

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

The surface area of a sphere is .  What is the diameter of the sphere?

Explanation:

The surface area of a sphere is given by

So the equation to sovle becomes  or so

To answer the question we need to find the diameter:

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

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

Explanation:

Write the formula for the volume of a sphere:

Plug in the volume and find the radius by solving for :

Start solving for  by multiplying both sides of the equation by :

Now, divide each side of the equation by :

Reduce the left side of the equation:

Finally, take the cubed root of both sides of the equation:

Keep in mind that you've solved for the radius, not the diameter. The diameter is double the radius, which is: .

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

The circumference of a sphere is . Find the radius.

Explanation:

If the circumference of a sphere is , that means we can easily solve for the diameter by using . This is the equation to find the circumference.

By substituting in the value for circumference (), we can solve for the missing variable

To find the radius of the sphere, we need to divide this value by :

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

Find the diameter of a sphere if the volume is .

Explanation:

Write the formula for the volume of a sphere.

Plug in the given volume and solve for the radius.

The diameter is double the radius.

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

Find the diameter of a sphere if the volume is .

Explanation:

Write the volume for the sphere.

Substitute the volume and solve for the radius.

Double the radius to find diameter.

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

Find the diameter of a sphere with the volume listed below.

Explanation:

In order to solve, we must the given volume into the volume formula for a sphere.

Divide both sides by pi.

Multiply both sides by 3.

Take the cube root of both sides to find the radius.

Double the radius to get the diameter, diameter is 12.

### Example Question #7 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of .

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

### Example Question #8 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of .

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

### Example Question #9 : How To Find The Diameter Of A Sphere

Find the diameter of the sphere if it has a volume of .

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

### Example Question #10 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of .

Explanation:

Recall how to find the volume of a sphere:

, where  is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

, where  is the diameter of the sphere.

Rewrite the equation to solve for .

Now, plug in the volume of the sphere to find the diameter.

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