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# Volume Word Problems Study Guide (page 2)

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Updated on Oct 4, 2011

## Volume of a Pyramid

A pyramid is a geometric solid with a polygon as a base and triangles as each of the other faces. A square base pyramid is shown in the following figure.

The volume of a pyramid is equal to one-third of the volume of a prism with the same dimensions. Therefore, the formula for the volume of a pyramid is equal to V = Bh, where B is the area of the base and h is the height of the pyramid.

#### Example

What is the volume of a square base pyramid with a base area of 25 cm2and a height of 15 cm?

Read and understand the question. This question is looking for the area of a square base pyramid when the area of the base and the height of the pyramid are known.

Make a plan. Use the formula V = Bh, where B is the area of the base and h is the height of the pyramid. Substitute the values and evaluate the formula.

Carry out the plan. The formula becomes

V = (25)(15)
= (375) = 125

The volume is 125 cm3.

Check your answer. To check your answer, work backward. Multiply the volume by 3, and then divide by one of the dimensions to check to see if the result is the other dimension.

125 × 3 = 375
375 ÷ 15 = 25

This result is checking.

## Solids With Curved Surfaces

The next two solids have curved surfaces, and each has one or two bases that are circles.

#### Tip:

Remember that the area of a circle is A = πr2. This formula is used to find the volume of the next two solids with bases in the shape of circles.

## Volume of a Cylinder

As mentioned in the previous lesson, a cylinder is a solid with two circles as the bases. To find the volume of a cylinder, multiply the area of the base by the height of the cylinder. Because the base is a circle, the formula is V = πr2h, where r is the radius of the base and h is the height of the cylinder.

#### Example

The radius of the base of a cylinder is 6 m and the height of the cylinder is 9 m. What is the volume of the cylinder in terms of π?

Read and understand the question. This question is looking for the volume of a cylinder when the radius of the base and the height are known.

Make a plan. Substitute into the volume formula, and then evaluate to find the volume.

Carry out the plan. The formula becomes V = π(6)2(9). Evaluate the exponent to get V = 36(9)π. Multiply to simplify. The volume is 324π m3.

Check your answer. To check this solution, use the strategy of working backward and divide the volume by the height times π. Then, take the positive square root to see if this result is the radius of the base: 324π ÷ 9π = 36. The positive square root of 36 is 6, which is the radius of the base. This answer is checking.

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