Question

Tall cylinder
Height 6
Base 2
Short cylinder
Height 2
Base 4

Which cylinder has the greater volume?

Short cylinder
Tall cylinder
Same volume

Answer 1

To find out which cylinder has a greater volume, we can use the formula for the volume of a cylinder:

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

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

1. **Volume of the Tall Cylinder:**
- Height (\( h \)) = 6
- Base diameter = 2, so the radius (\( r \)) = 2 / 2 = 1
\[
V_{\text{tall}} = \pi (1^2)(6) = \pi (1)(6) = 6\pi
\]

2. **Volume of the Short Cylinder:**
- Height (\( h \)) = 2
- Base diameter = 4, so the radius (\( r \)) = 4 / 2 = 2
\[
V_{\text{short}} = \pi (2^2)(2) = \pi (4)(2) = 8\pi
\]

Now, comparing the two volumes:
- Volume of the tall cylinder = \( 6\pi \)
- Volume of the short cylinder = \( 8\pi \)

Since \( 8\pi > 6\pi \), the **Short Cylinder** has the greater volume.