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

1 answer

To determine whether the statement is true or false, 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,
  • \( h \) is the height.

Given:

  • Radius \( r = 4 \) inches,
  • Height \( h = 16 \) inches.

Now we can calculate the volume:

\[ V = \pi (4)^2 (16) \] \[ = \pi (16)(16) \] \[ = 256\pi \]

Next, we can compute \( 256\pi \) using an approximate value of \( \pi \approx 3.14 \):

\[ V \approx 256 \times 3.14 \approx 804.16 \text{ cubic inches} \]

Since the calculated volume is approximately \( 804.16 \) cubic inches and not \( 604.56 \) cubic inches,

the statement is false.