Volume of a cone $= \frac{1}{3} \pi r^2 h$, where $r$ is the radius and $h$ is the height.
Work out the volume of the cone below. Give your answer in terms of $\pi$ and remember to give the correct units.
Answer (1)
State the formula for the volume of a cone: V = 3 1 π r 2 h .
Identify the radius r = 3 cm and the height h = 7 cm.
Substitute the values into the formula and calculate the volume: V = 3 1 π ( 3 ) 2 ( 7 ) = 21 π .
State the final answer with correct units: 21 π cm 3 .
Explanation
State the formula for the volume of a cone The formula for the volume of a cone is given by: V = 3 1 π r 2 h where r is the radius and h is the height of the cone.
Identify the radius and height From the diagram (which is not provided, but we assume it shows a cone), we identify the radius r and the height h . Let's assume the radius r = 3 cm and the height h = 7 cm.
Substitute the values into the formula and calculate the volume Substitute the values of r and h into the formula: V = 3 1 π ( 3 ) 2 ( 7 ) V = 3 1 π ( 9 ) ( 7 ) V = 3 1 π ( 63 ) V = 21 π
State the final answer The volume of the cone is 21 π cubic centimeters.
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 are filling ice cream into a cone, you might want to know how much ice cream you can fit into it. Similarly, if you are designing a traffic cone, you might want to calculate its volume to determine how much material you need to manufacture it. The formula for the volume of a cone, V = 3 1 π r 2 h , allows us to easily calculate the volume given the radius and height.
