# ISEE Upper Level Math : Spheres

## Example Questions

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### Example Question #1 : Spheres

There is a perfectly spherical weather balloon with a surface area of  , what is its diameter?

Explanation:

There is a perfectly spherical weather balloon with a surface area of  , what is its diameter?

Begin with the formula for surface area of a sphere:

Now, set it equal to the given surface area and solve for r:

First divide both sides by .

Then square root both sides to get our radius:

Now, because the question is asking for our diameter and not our radius, we need to double our radius to get our answer:

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

A wooden ball has a surface area of .

Cannot be determined from the information provided

Explanation:

A wooden ball has a surface area of .

Begin with the formula for surface area of a sphere:

Now, plug in our surface area and solve with algebra:

Get rid of the pi

Divide by 4

Square root both sides to get our answer:

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

There is a perfectly spherical weather balloon with a surface area of  , what is its radius?

Explanation:

There is a perfectly spherical weather balloon with a surface area of  , what is its radius?

Begin with the formula for surface area of a sphere:

Now, set it equal to the given surface area and solve for r:

First divide both sides by .

Then square root both sides to get our answer:

### Example Question #1 : Spheres

In terms of , give the volume, in cubic inches, of a spherical water tank with a diameter of 20 feet.

Explanation:

20 feet =  inches, the diameter of the tank; half of this, or 120 inches, is the radius. Set , substitute in the volume formula, and solve for :

cubic inches

### Example Question #2 : Spheres

A sphere has diameter 3 meters. Give its volume in cubic centimeters (leave in terms of ).

Explanation:

The diameter of 3 meters is equal to  centimeters; the radius is half this, or 150 centimeters. Substitute  in the volume formula:

cubic centimeters

### Example Question #79 : Solid Geometry

A spherical buoy has a radius of 5 meters. What is the volume of the buoy?

Explanation:

A spherical buoy has a radius of 5 meters. What is the volume of the buoy?

To find the volume of a sphere, use the following formula:

All we have to do is plug in 5 meters and simplify:

### Example Question #80 : Solid Geometry

You have a ball with a radius of  12 cm, what is its volume?

Explanation:

You have a ball with a radius of  12 cm, what is its volume?

The volume of a sphere can be found via the following formula:

We know our radius, so all we need to do is plug in and simplify:

### Example Question #81 : Solid Geometry

You have a wooden ball which you are going to paint. If the radius is 12 inches, what is the volume of the ball?

Explanation:

You have a wooden ball which you are going to paint. If the radius is 12 inches, what is the volume of the ball?

Alright, let's begin with the volume of a sphere formula:

Now, plug in 12 and simplify:

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

Find the volume of a sphere with a diameter of 6cm.

Explanation:

To find the volume of a sphere, we will use the following formula:

where r is the radius of the sphere.

Now, we know the diameter of the sphere is 6cm.  We also know that the diameter is two times the radius.  Therefore, the radius is 3cm.

Knowing this, we can substitute into the formula.  We get

Now, before we continue, we can simplify.  The 3 and the 27 can both be divided by 3.  We get

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

Find the volume of a sphere with a diameter of 12in.

Explanation:

To find the volume of a sphere, we will use the following formula:

where r is the radius of the sphere.

Now, we know the diameter of the sphere is 12in.  We also know the diameter is two times the radius.  Therefore, the radius is 6in.

Knowing this, we can substitute into the formula.  We get

Now, we can simplify before we multiply to make things easier. The 3 and a 6 can both be divided by 3.  So, we get

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