Question

what's the same volume of the cylinders; left cylinder h=2 d=3./ Right cylinder H=6 D=3

Answer 1

To compare the volumes of the two cylinders, we will use the formula for the volume of a cylinder:

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

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

### Left Cylinder:
- Height \( h = 2 \)
- Diameter \( d = 3 \) (which means the radius \( r = \frac{d}{2} = \frac{3}{2} = 1.5 \))

Now, let's calculate the volume:

\[
V_{\text{left}} = \pi (1.5)^2 (2) = \pi (2.25)(2) = 4.5\pi
\]

### Right Cylinder:
- Height \( H = 6 \)
- Diameter \( D = 3 \) (which means the radius \( R = \frac{D}{2} = \frac{3}{2} = 1.5 \))

Now, let's calculate this volume as well:

\[
V_{\text{right}} = \pi (1.5)^2 (6) = \pi (2.25)(6) = 13.5\pi
\]

### Conclusion:
- Volume of the left cylinder: \( 4.5\pi \)
- Volume of the right cylinder: \( 13.5\pi \)

Thus, the cylinders do not have the same volume; the right cylinder has three times the volume of the left cylinder.