Question

You are comparing two cylindrical containers. Cylinder 1 has a volume of 360𝝅
and a base radius of 6. Cylinder 2 has a volume of 400𝝅
and a radius of 10. Which container is taller? How do you know?

Answer 1

To determine which cylindrical container is taller, we can use the formula for the volume of a cylinder, which is given by:

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

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

### Cylinder 1:
- Volume \( V_1 = 360\pi \)
- Radius \( r_1 = 6 \)

We can solve for the height \( h_1 \) of Cylinder 1:

\[
360\pi = \pi (6^2) h_1
\]

By simplifying, we can cancel \( \pi \):

\[
360 = 36 h_1
\]

Now divide both sides by 36:

\[
h_1 = \frac{360}{36} = 10
\]

So, the height of Cylinder 1 is \( h_1 = 10 \).

### Cylinder 2:
- Volume \( V_2 = 400\pi \)
- Radius \( r_2 = 10 \)

Now, we can solve for the height \( h_2 \) of Cylinder 2:

\[
400\pi = \pi (10^2) h_2
\]

Cancel \( \pi \):

\[
400 = 100 h_2
\]

Now divide both sides by 100:

\[
h_2 = \frac{400}{100} = 4
\]

So, the height of Cylinder 2 is \( h_2 = 4 \).

### Conclusion:
Now we compare the heights:

- Height of Cylinder 1: \( h_1 = 10 \)
- Height of Cylinder 2: \( h_2 = 4 \)

Thus, Cylinder 1 is taller than Cylinder 2.