What is the volume of a cylinder with a radius of 3 cm and a height of 10 cm? (Use the formula V = πr²h)
Understand the Problem
The question is asking us to calculate the volume of a cylinder using the formula for the volume of a cylinder, which is V = πr²h, where r is the radius and h is the height. We will insert the given values (radius of 3 cm and height of 10 cm) into the formula.
Answer
The volume of the cylinder is $90\pi \text{ cm}^3$ or approximately $282.6 \text{ cm}^3$.
Answer for screen readers
The volume of the cylinder is $V = 90\pi \text{ cm}^3$ or approximately $282.6 \text{ cm}^3$.
Steps to Solve
- Identify the formula for the volume of a cylinder
We know the formula for the volume of a cylinder is given by:
$$ V = \pi r^2 h $$
where $r$ is the radius and $h$ is the height of the cylinder.
- Insert the given values into the formula
Given radius $r = 3$ cm and height $h = 10$ cm, we substitute these values into the formula:
$$ V = \pi (3)^2 (10) $$
- Calculate the radius squared
First, we calculate $3^2$:
$$ 3^2 = 9 $$
So, we can update our expression for volume to:
$$ V = \pi (9)(10) $$
- Multiply the radius squared by the height
Next, we multiply $9$ by $10$:
$$ 9 \times 10 = 90 $$
Now, we have:
$$ V = \pi (90) $$
- Calculate the volume
Finally, we can express the volume as:
$$ V = 90\pi $$
For an approximate numerical value, we use $ \pi \approx 3.14$:
$$ V \approx 90 \times 3.14 = 282.6 \text{ cm}^3 $$
The volume of the cylinder is $V = 90\pi \text{ cm}^3$ or approximately $282.6 \text{ cm}^3$.
More Information
The volume of a cylinder is crucial in various applications, such as calculating the capacity of containers. The formula we used involves basic operations like squaring a number and multiplying. Approximating $\pi$ helps to find a numerical solution for practical use.
Tips
- Not squaring the radius before multiplying by the height. Ensure the $r^2$ is calculated first.
- Forgetting to include the units in the final answer. Always mention the units such as cm³.