volume of a cone $= \frac{1}{3} \pi r^2 h$, where $r$ is the radius and $h$ is the height.
What is the volume of the cone below?
Give your answer in terms of $\pi$.
Answer (1)
Substitute the given radius r = 3 and height h = 8 into the cone volume formula: V = 3 1 π r 2 h .
Calculate 3 2 = 9 , then multiply by 8 to get 9 × 8 = 72 .
Divide 72 by 3 to find the volume: 3 72 = 24 .
State the final volume in terms of π : 24 π .
Explanation
Problem Setup and Given Information We are given the formula for the volume of a cone: V = 3 1 π r 2 h , where r is the radius and h is the height. We are also given that the radius r = 3 and the height h = 8 . We need to find the volume of the cone in terms of π .
Substitute Values Substitute the given values of r and h into the formula for the volume of a cone:
V = 3 1 π ( 3 2 ) ( 8 )
Calculate the Square First, calculate 3 2 = 9 . So the equation becomes:
V = 3 1 π ( 9 ) ( 8 )
Multiply Now, multiply 9 and 8: 9 × 8 = 72 . So the equation becomes:
V = 3 1 π ( 72 )
Divide Finally, divide 72 by 3: 3 72 = 24 . So the volume of the cone is:
V = 24 π
Examples
Cones are common shapes in everyday life, from ice cream cones to traffic cones. Knowing how to calculate the volume of a cone can be useful in many practical situations. For example, if you're filling ice cream cones at a party, you can use the volume formula to estimate how much ice cream you'll need. Similarly, engineers and architects use the volume formula to calculate the amount of material needed to construct conical structures, such as roofs or funnels. Understanding cone volume helps in efficient material usage and cost estimation.
