# GED Math : 3-Dimensional Geometry

## Example Questions

### Example Question #1 : 3 Dimensional Geometry

A water tank takes the shape of a sphere whose exterior has radius 18 feet; the tank is three inches thick throughout. To the nearest hundred, how many cubic feet of water does the tank hold?

Use 3.14 for .

Explanation:

Three inches is equal to 0.25 feet, so the radius of the interior of the tank is

feet.

The amount of water the tank holds is the volume of the interior of the tank, which is

,

which rounds to 23,400 cubic feet.

### Example Question #1 : Volume Of A Sphere

The contents of a full spherical glass 3 inches in radius are poured into an empty cylindrical glass 6 inches in radius and 6 inches high. What percent of the cylindrical glass is taken up by the contents?

Explanation:

The volume of the spherical glass is

where :

The volume of the cylindrical glass is

,

where :

The contents of the spherical glass will take up

of the capacity of the cylindrical glass.

### Example Question #3 : Volume Of A Sphere

The contents of a full cylindrical glass 4 inches in radius and 8 inches high are poured into an empty spherical glass 6 inches in radius. What percent of the spherical glass is taken up by the contents?

Explanation:

The volume of the cylindrical glass is

,

where :

The volume of the spherical glass is

where :

The contents of the cylindrical glass will take up

of the capacity of the spherical glass.

### Example Question #551 : Geometry And Graphs

Find the volume of the sphere with a diameter of 5.

Explanation:

Write the formula for the volume of a sphere.

Substitute the radius, which is half the diameter.

Simplify the terms.

### Example Question #1 : 3 Dimensional Geometry

Determine the volume of a sphere with a radius of 5.

Explanation:

Write the formula for the volume of a sphere.

Substitute the radius into the formula.

### Example Question #1 : 3 Dimensional Geometry

Determine the volume of a sphere if the diameter is .

Explanation:

Write the formula for the volume of the sphere.

Substitute the radius into the formula.

Any value cubed rooted that is raised to the power of three will leave only the integer behind.

### Example Question #7 : Volume Of A Sphere

Determine the volume of a sphere with a diameter of 3.

Explanation:

Given the diameter is 3, the radius is half the diameter, or .

Write the formula for the volume of a circle.

Reduce the fractions.

### Example Question #8 : Volume Of A Sphere

Determine the volume of a sphere if the diameter is .

Explanation:

Write the formula for the volume of a sphere.

The radius is half the diameter.

### Example Question #9 : Volume Of A Sphere

Find the volume of a sphere if the radius of the sphere is .

Explanation:

Write the volume formula for the sphere.

Substitute the radius into the formula.

Simplify the terms.

### Example Question #10 : Volume Of A Sphere

Let

A sphere has a radius of 3in. Find the volume.

Explanation:

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

where r is the radius of the sphere.

We know .

We know the radius of the sphere is 3in.

Now, we can substitute. We get

Now, we can simplify to make things easier. The 3 and the 27 can both be divided by 3. So, we get