Question

Left cylinder
height 8
radius 8
Right cylinder
height 4
radius 8

What is the volume of the cylinders?

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, and \( h \) is the height.

### For the Left Cylinder:
- Height (\( h_1 \)) = 8
- Radius (\( r \)) = 8

\[
V_1 = \pi (8)^2 (8) = \pi (64)(8) = 512\pi
\]

### For the Right Cylinder:
- Height (\( h_2 \)) = 4
- Radius (\( r \)) = 8

\[
V_2 = \pi (8)^2 (4) = \pi (64)(4) = 256\pi
\]

### Total Volume:
To find the total volume of both cylinders, you can add the two volumes together:

\[
V_{\text{total}} = V_1 + V_2 = 512\pi + 256\pi = 768\pi
\]

### Final Result:
The volumes of the cylinders are as follows:
- Left Cylinder: \( 512\pi \)
- Right Cylinder: \( 256\pi \)
- Total Volume: \( 768\pi \)

If you need a numerical approximation, using \( \pi \approx 3.14 \):

\[
768\pi \approx 768 \times 3.14 \approx 2411.52
\]

Therefore, the total volume of both cylinders is approximately \( 2411.52 \) cubic units.