# ISEE Upper Level Math : How to find the surface area of a sphere

## Example Questions

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

In terms of , give the surface area, in square feet, of a spherical tank with diameter 36 inches.

Explanation:

36 inches =  feet, the diameter of the tank. Half of this, or  feet, is the radius. Set , substitute in the surface area formula, and solve for :

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

Give the surface area of a sphere with diameter .

Explanation:

A sphere with diameter  has radius half that, or , so substitute  into the formula for the surface area of a sphere:

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

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

Explanation:

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

To find the surface area of a sphere, use the following:

Plug in our radius and solve!

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

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

Not enough information provided

Explanation:

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

First, recall the formula for surface area of a sphere:

Now, just plug in our known radius and simplify:

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

Find the surface area of a sphere with a diameter of 10in.

Explanation:

To find the surface area 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 10cm.  We also know the diameter is two times the radius.  Therefore, the radius is 5cm.

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

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

Find the surface area of a sphere with a radius of 10in.

Explanation:

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

where r is the radius of the sphere.

Now, we know the radius of the sphere is 10in.

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

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

Find the surface area of a sphere with a diameter of 18in.

Explanation:

To find the surface area 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 18in.  We also know the diameter is two times the radius.  Therefore, the radius is 9in.

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

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

Find the surface area of a sphere with a radius of 6in.

Explanation:

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

where r is the radius of the sphere.

Now, we know the radius of the sphere is 6in.  Knowing this, we can substitute into the formula.  We get

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

Find the surface area of a sphere with a radius of 12in.

Explanation:

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

where r is the radius of the sphere.

Now, we know the radius of the sphere is 12in.

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

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

Find the surface area of a sphere with a diameter of 20in.

Explanation:

To find the surface area 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 20in.  We also know the diameter is two times the radius.  Therefore, the radius is 10in.

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

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