Question

Find the volume of this cylinder in terms of pi. You can solve on paper and enter your answer on Zearn.
3 cm
6 cm
V = B · h
Volume = Area of base · Height
= πr
2
· h
= cm
3

Answer 1

To find the volume of a cylinder, we use the formula:

\[
V = B \cdot h
\]

where \(B\) is the area of the base and \(h\) is the height of the cylinder.

The base of the cylinder is a circle, and its area \(B\) can be calculated using the formula:

\[
B = \pi r^2
\]

where \(r\) is the radius of the base.

Given that the diameter of the cylinder is 6 cm, we can find the radius:

\[
r = \frac{\text{diameter}}{2} = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm}
\]

Now, we can calculate the area of the base:

\[
B = \pi r^2 = \pi (3 \, \text{cm})^2 = \pi \cdot 9 \, \text{cm}^2 = 9\pi \, \text{cm}^2
\]

Next, we need to multiply the area of the base by the height of the cylinder to find the volume. The height of the cylinder is given as 3 cm:

\[
V = B \cdot h = 9\pi \, \text{cm}^2 \cdot 3 \, \text{cm} = 27\pi \, \text{cm}^3
\]

Thus, the volume of the cylinder is:

\[
\boxed{27\pi} \, \text{cm}^3
\]