**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.

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* = π*r*^{2}*h*.

ExampleWhat 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* = π*r*^{2}*h* 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* = π*r*^{3}, where *r* is the radius of the sphere.

ExampleWhat 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 6^{3}.

- 288π ÷ π = 216

- 6

^{3}is 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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