Question

A cylindrical water bottle has a height of 16 inches and a radius of 4 inches.
True or false: This cylinder has a volume of 604.56 cubic inches.

Answer 1

To determine if the statement is true or false, we need to calculate the volume of the cylindrical water bottle using the formula for the volume of a cylinder:

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

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14159.

Given:
- Height \( h = 16 \) inches,
- Radius \( r = 4 \) inches.

Now we can substitute these values into the formula:

\[
V = \pi (4^2)(16)
\]
\[
V = \pi (16)(16)
\]
\[
V = \pi (256)
\]
\[
V \approx 3.14159 \times 256 \approx 804.25 \text{ cubic inches}
\]

Thus, the volume is approximately 804.25 cubic inches, not 604.56 cubic inches.

Therefore, the statement is **false**.