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 $282.6 \text{ cm}^3$.

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.

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