What is the volume of the cylinder when its radius is tripled, given that it originally has a radius of 4 centimeters and a height of 5 centimeters?
Understand the Problem
The question asks us to calculate the new volume of a cylinder when its radius is tripled, given its original radius and height. We will first calculate the original volume and then calculate the new volume after tripling the radius using the formula V = πr²h.
Answer
$720\pi \text{ cm}^3$
Answer for screen readers
$720\pi \text{ cm}^3$
Steps to Solve
- Calculate the original volume
The original volume of a cylinder is given by the formula $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height. Given $r = 4$ cm and $h = 5$ cm, we have:
$V = \pi (4)^2 (5) = \pi (16)(5) = 80\pi$ cubic centimeters.
- Triple the radius
The new radius is three times the original radius:
$r_{new} = 3 \times 4 = 12$ cm.
- Calculate the new volume
Using the same formula $V = \pi r^2 h$ with the new radius $r_{new} = 12$ cm and the same height $h = 5$ cm, we have:
$V_{new} = \pi (12)^2 (5) = \pi (144)(5) = 720\pi$ cubic centimeters.
$720\pi \text{ cm}^3$
More Information
The volume increased significantly when the radius was tripled because the radius is squared in the volume formula.
Tips
A common mistake is to triple the original volume instead of calculating the new volume with the tripled radius. Remember that the radius is squared in the formula, which significantly affects the new volume.
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