Calculate the volume of a cylinder with a radius of 12 and a height of 5.
Understand the Problem
The question is asking us to calculate the volume of a cylinder given its radius and height. We will use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius and h is the height.
Answer
$V = 63\pi \text{ cm}^3$ or $V \approx 197.82 \text{ cm}^3$
Answer for screen readers
The volume of the cylinder is $63\pi \text{ cm}^3$. The approximate volume is $197.82 \text{ cm}^3$.
Steps to Solve
- Write down the formula for the volume of a cylinder
The volume $V$ of a cylinder is given by the formula:
$$V = \pi r^2 h$$
where $r$ is the radius and $h$ is the height.
- Substitute the given values into the formula
We are given that the radius $r = 3$ cm and the height $h = 7$ cm. Substituting these values into the formula, we get:
$$V = \pi (3)^2 (7)$$
- Calculate the volume
$$V = \pi (9)(7)$$
$$V = 63\pi$$
Therefore, the volume of the cylinder is $63\pi$ cubic centimeters.
- Approximate the volume using $\pi \approx 3.14$
If we want a numerical approximation, we can use $\pi \approx 3.14$:
$$V \approx 63 \times 3.14 = 197.82$$
So, the approximate volume is $197.82$ cubic centimeters.
The volume of the cylinder is $63\pi \text{ cm}^3$. The approximate volume is $197.82 \text{ cm}^3$.
More Information
The volume is expressed in cubic units because it's a three-dimensional measurement. Leaving the answer in terms of $\pi$ is often more accurate, unless a decimal approximation is specifically requested.
Tips
A common mistake is to confuse the formula for the volume of a cylinder with the formula for the surface area of a cylinder or the area of a circle. Another mistake is to forget to square the radius in the volume formula. Also, forgetting the units or using the wrong units is a common mistake.
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