Question

a cy;ider with a hight of 6 and base 1 and the 2nd cylinder with a hight of 2 and base of 2 what r the volume of the both 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 of the base, and \( h \) is the height of the cylinder.

1. **For the first cylinder**:
- Height (\( h_1 \)) = 6
- Base radius (\( r_1 \)) = 1 (the diameter is 2, so radius is half of that)

The volume is:
\[
V_1 = \pi (1)^2 (6) = 6\pi
\]

2. **For the second cylinder**:
- Height (\( h_2 \)) = 2
- Base radius (\( r_2 \)) = 2 (the diameter is 4, so radius is half of that)

The volume is:
\[
V_2 = \pi (2)^2 (2) = 8\pi
\]

3. **Total volume of both cylinders**:
\[
V_{total} = V_1 + V_2 = 6\pi + 8\pi = 14\pi
\]

So the volumes of the cylinders are:
- First cylinder: \( 6\pi \)
- Second cylinder: \( 8\pi \)
- Total volume: \( 14\pi \) (approximately 43.98 cubic units using \( \pi \approx 3.14 \)).