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

## Example Questions

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### Example Question #1 : Spheres

A sphere has a circumference of , what is its volume?

Explanation:

The circumference is given by  which yields a radius of 4.  The volume is given by

### Example Question #2 : Spheres

Explanation:

Simplified, it is

### Example Question #1 : Spheres

What is the volume of a sphere with a diameter of 6 in?

Explanation:

The formula for the volume of a sphere is:

where  = radius.  The diameter is 6 in, so the radius will be 3 in.

### Example Question #1 : Spheres

The circumference of a sphere is . What is the sphere's volume?

Explanation:

The formula to find the volume of a sphere is:

Finding the volume is simple. All that we need is the radius!

The only information the problem provides is the circumference. In order to find the radius, we have to think how circumference relates to radius.

Since the equation for circumference is , where d stands for diameter, and radius is half of the diameter, the two have diameter in common.

The first step in solving this problem is to determine the diameter from the circumference:

Because the diameter is , the radius must be

Now we are ready to solve for the volume after substituting in our  value.

### Example Question #4 : Spheres

A cube with a side length of 20 inches has a sphere inscribed within. What is the volume of the sphere?

Explanation:

The cube has a side length of 20 inches. Since the sphere is inscribed within the cube its diameter measures 20 inches; the radius will be 10 inches.

The volume of a sphere is given by

.

### Example Question #5 : Spheres

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , find the volume of the figure.

Explanation:

Recall how to find the volume of a sphere:

Now since we only have half a sphere, divide the volume by .

Plug in the given radius to find the volume of the figure.

Make sure to round to  places after the decimal.

### Example Question #6 : Spheres

A sphere is cut in half as shown by the figure below.

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

Explanation:

Recall how to find the volume of a sphere:

Now since we only have half a sphere, divide the volume by .

Plug in the given radius to find the volume of the figure.

Make sure to round to  places after the decimal.

### Example Question #7 : Spheres

A sphere is cut in half as shown by the figure below.

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

Explanation:

Recall how to find the volume of a sphere:

Now since we only have half a sphere, divide the volume by .

Plug in the given radius to find the volume of the figure.

Make sure to round to  places after the decimal.

### Example Question #8 : Spheres

A sphere is cut in half as shown by the figure below.

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

Explanation:

Recall how to find the volume of a sphere:

Now since we only have half a sphere, divide the volume by .

Plug in the given radius to find the volume of the figure.

Make sure to round to  places after the decimal.

### Example Question #9 : Spheres

A sphere is cut in half as shown by the figure below.

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