# GED Math : Volume of Other Solids

## Example Questions

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### Example Question #1 : Volume Of Other Solids

The above depicts a rectangular swimming pool for an apartment.

On the right edge, the pool is three feet deep; on the left edge, it is eight feet deep. Going from the right to the left, its depth increases uniformly. In cubic feet, how much water does the pool hold?

Explanation:

The pool can be looked at as a trapezoidal prism with "height" 35 feet and its bases the following shape (depth exaggerated):

The area of this trapezoidal base, which has height 50 feet and bases 3 feet and 8 feet, is

square feet;

The volume of the pool is the base multiplied by the "height", or

cubic feet, the capacity of the pool.

### Example Question #2 : Volume Of Other Solids

Refer to the right circular cone in the above diagram. What is its volume, to the nearest whole cubic centimeter?

Explanation:

The volume of a right circular cone of height  and base with radius  is

.

The radius is 50. To find the height, we need to use the Pythagorean Theorem with the radius 50 as one leg and the slant height 130 as the hypotenuse of a right triangle, and the height  as the other leg:

Substitute 120 for  and 50 for  in the volume formula:

cubic centimeters.

### Example Question #3 : Volume Of Other Solids

Find the volume of a cube with a height of 12cm.

Explanation:

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

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 12cm. Because it is a cube, all sides (lengths, widths, heights) are equal. Therefore, the length and the width are also 12cm. So, we can substitute. We get

### Example Question #4 : Volume Of Other Solids

A cone has a diameter of 10in and a height of 6in.  Find the volume.

Explanation:

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

where r is the radius and h is the height of the cone.

Now, we know the diameter of the cone is 10in. We also know the diameter is two times the radius. Therefore, the radius is 5in.

We know the height of the cone is 6in.

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

### Example Question #5 : Volume Of Other Solids

Find the volume of a cube with a height of 11in.

Explanation:

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

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 11in. Because it is a cube, all sides are equal. Therefore, the width and the length are also 11in. So, we can substitute. We get

### Example Question #1 : Volume Of Other Solids

Find the volume of a cube with a height of 10cm.

Explanation:

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

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 10cm. Because it is a cube, all sides (lengths, widths, heights) are equal. Therefore, the length and the width are also 10cm. So, we can substitute. We get

### Example Question #7 : Volume Of Other Solids

A cone has a diameter of 8in and a height of 9in. Find the volume.

Explanation:

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

where r is the radius and h is the height of the cone.

Now, we know the diameter of the cone is 8in. We also know the diameter is two times the radius. Therefore, the radius is 4in.

We know the height of the cone is 9in.

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

### Example Question #8 : Volume Of Other Solids

Find the volume of a cube with a height of 7in.

Explanation:

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

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 7in. Because it is a cube, all sides are equal. Therefore, the width and the length are also 7in. So, we can substitute. We get

### Example Question #1 : Volume Of Other Solids

Let .

A cone has a height of 5in and a diameter of 12in. Find the volume.

Explanation:

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

where r is the radius and h is the height of the cone.

We know .

We know the diameter of the cone is 12in. We know the diameter is two times the radius. So, the radius is 6in.

We know the height is 5in.

Now, we can substitute. We get

Now, we can simplify to make things easier. The 36 and the 3 can both be divided by 3. So, we get

### Example Question #1 : Volume Of Other Solids

If a cube has a width of 7in, find the volume.