If the volume of a cylinder is 150 cubic centimeters and the height is 10 cm, what is the radius of the base?

Question

UpStudy AI · Accepted Answer

To find the radius of the base of a cylinder given its volume and height, we can use the formula for the volume of a cylinder:

$$
V = \pi r^2 h
$$

where:
- $$ V $$ is the volume,
- $$ r $$ is the radius of the base,
- $$ h $$ is the height.

Given:
- $$ V = 150 $$ cubic centimeters,
- $$ h = 10 $$ cm.

We can rearrange the formula to solve for $$ r $$:

$$
r^2 = \frac{V}{\pi h}
$$

Substituting the known values into the equation:

$$
r^2 = \frac{150}{\pi \times 10}
$$

$$
r^2 = \frac{150}{10\pi}
$$

$$
r^2 = \frac{15}{\pi}
$$

Now, we can find $$ r $$ by taking the square root of both sides:

$$
r = \sqrt{\frac{15}{\pi}}
$$

Using the approximate value of $$ \pi \approx 3.14 $$:

$$
r = \sqrt{\frac{15}{3.14}} \approx \sqrt{4.78} \approx 2.19 \text{ cm}
$$

Thus, the radius of the base of the cylinder is approximately $$ 2.19 $$ cm.
The radius of the base is approximately 2.19 cm.

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