# Intermediate Geometry : Spheres

## Example Questions

### Example Question #71 : Spheres

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.

Make sure to round to  places after the decimal.

### Example Question #72 : Spheres

Find the diameter of a sphere that 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.

Make sure to round to  places after the decimal.

### Example Question #11 : 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.

Make sure to round to  places after the decimal.

### Example Question #74 : Spheres

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.

Make sure to round to  places after the decimal.

### Example Question #75 : Spheres

Find the diameter of a sphere if its volume is .

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.

Make sure to round to  places after the decimal.

### Example Question #76 : Spheres

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.

Make sure to round to  places after the decimal.

### Example Question #77 : Spheres

A company wants to construct an advertising balloon spherical in shape. It can afford to buy 28,000 square meters of material to make the balloon. What is the largest possible diameter of this balloon (nearest whole meter)?

Explanation:

This is equivalent to asking the diameter of a balloon with surface area 28,000 square meters.

The relationship between the surface area  and the radius  is:

To find the radius, substitute for the surface area, then solve:

To find the diameter , double the radius—this is 94.

### 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 #2 : 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?