Question

Order the cylinders from greatest volume (put at the top of the list) to least volume (put at the bottom of the list).

r h 2r h r 3h

(3 points)
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Answer 1

To determine the volume of each cylinder, we use the formula for the volume of a cylinder, which is:

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

1. **Cylinder 1: radius \( r \) and height \( h \)**
\[
V_1 = \pi r^2 h
\]

2. **Cylinder 2: radius \( 2r \) and height \( h \)**
\[
V_2 = \pi (2r)^2 h = \pi (4r^2) h = 4\pi r^2 h
\]

3. **Cylinder 3: radius \( r \) and height \( 3h \)**
\[
V_3 = \pi r^2 (3h) = 3\pi r^2 h
\]

Now we can compare the volumes:

- \( V_1 = \pi r^2 h \)
- \( V_2 = 4\pi r^2 h \)
- \( V_3 = 3\pi r^2 h \)

Ordering from greatest to least volume gives us:

1. \( V_2 = 4\pi r^2 h \) (greatest)
2. \( V_3 = 3\pi r^2 h \)
3. \( V_1 = \pi r^2 h \) (least)

So the correct order from greatest volume to least volume is:

1. \( 2r, h \)
2. \( r, 3h \)
3. \( r, h \)