Question

The height of a cylinder is 6 centimeters. The circumference of the base of the cylinder is 14𝜋 centimeters.







Which measurement is closest to the volume of the cylinder in cubic centimeters.
Responses

A 3,694.5 cm³3,694.5 cm³

B 923.6 cm³923.6 cm³

C 395.84 cm³395.84 cm³

D 8,620.53 cm³

Answer 1

To calculate the volume of a cylinder, we can use the formula:

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

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

1. First, we need to find the radius of the base of the cylinder. We know the circumference \( C \) of the base:

\[
C = 2\pi r
\]

Given that \( C = 14\pi \):

\[
14\pi = 2\pi r
\]

To solve for \( r \), we can divide both sides by \( 2\pi \):

\[
r = \frac{14\pi}{2\pi} = 7 \text{ cm}
\]

2. Now we can find the volume using the height \( h = 6 \) cm and the radius \( r = 7 \) cm:

\[
V = \pi (7^2)(6)
\]
\[
V = \pi (49)(6)
\]
\[
V = 294\pi
\]

3. Now let's calculate \( 294\pi \) using the approximate value of \( \pi \):

\[
V \approx 294 \times 3.14 = 923.16 \text{ cm}^3
\]

The closest measurement to the volume of the cylinder is:

\[
\boxed{923.6 \text{ cm}^3}
\]

Thus, the correct answer is B: \( 923.6 \text{ cm}^3 \).