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Volume Word Problems Study Guide (page 3)

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Updated on Oct 4, 2011

Volume of a Cone

A cone is a solid with one base that is a circle. An example of a cone is shown in the following figure.

Cone

The volume of a cone is equal to one-third of the volume of a cylinder with the same height and the same size circular base. Therefore, the formula for the volume of a cone is V = πr2h.

Example

What is the volume of a cone with a base radius of 9 in. and a height of 5 in.?

Read and understand the question. This question is asking for the volume of a cone when the radius of the base and the height are given.

Make a plan. Use the formula V = πr2h and substitute the given values. Evaluate the formula to find the volume.

Carry out the plan. The formula becomes V = π(9)2(5). Evaluate the exponent to simplify to V = (81)(5)π. Multiply. V = (405)π. Divide 405 by 3 to simplify: V = 135π in.3.

Check your answer. To check this answer, work backward by multiplying the volume by 3. Then, divide by the height times π and take the positive square root of the result to get the length of the base radius:

    135π × 3 = 405π
    405π ÷ 5π = 81

The positive square root of 81 is 9, so this answer is checking.

Volume of a Sphere

The volume of a sphere can be found by using the formula V = πr3, where r is the radius of the sphere.

Example

What is the volume of a sphere with a radius of 6 in.?

Read and understand the question. This question is looking for the volume of a sphere when the radius is given.

Make a plan. Substitute the value of r into the formula and evaluate to find the volume.

Carry out the plan. The formula becomes V = π(6)3. Evaluate the exponent to get V = π(216). Multiply to get V = 288π in.3.

Check your answer. To check this result, divide the volume by π. Then, see if the result is the same as 63.

    288π ÷ π = 216
    63is also equal to 216, so this result is checking.

Find practice problems and solutions for these concepts at Volume Word Problems Practice Questions.

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