Question

what is the volume of a cylinder that has the height of 10, and the base 3.

Answer 1

To calculate the volume of a cylinder, you can use the formula:

\[
V = \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

From your information, the height \( h \) is 10, and it seems you mentioned the base as 3, which I will assume to be the diameter. To find the radius \( r \), you need to divide the diameter by 2:

\[
r = \frac{d}{2} = \frac{3}{2} = 1.5
\]

Now, plug the values into the volume formula:

\[
V = \pi (1.5)^2 (10)
\]

Calculating \( (1.5)^2 \):

\[
(1.5)^2 = 2.25
\]

Now plug this back into the volume formula:

\[
V = \pi (2.25)(10) = 22.5\pi
\]

Using \( \pi \approx 3.14 \) for the calculation:

\[
V \approx 22.5 \times 3.14 \approx 70.65
\]

So, the volume of the cylinder is approximately:

\[
22.5\pi \text{ cubic units, or } 70.65 \text{ cubic units (using } \pi \approx 3.14\text{)}.
\]