Question

The volume of a right circular cylinder is 7,693 cm3
. Find the height of the cylinder if the diameter is 14 cm. Use 3.14 for pi.(1 point)
Responses

12.5 cm
12.5 cm

175 cm
175 cm

39.25 cm
39.25 cm

50 cm

Answer 1

To find the height of the right circular cylinder, 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, and \( h \) is the height.

Given:
- Volume \( V = 7693 \, \text{cm}^3 \)
- Diameter \( d = 14 \, \text{cm} \)

First, we calculate the radius \( r \):

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

Now we can substitute the values into the volume formula and solve for \( h \):

\[
7693 = 3.14 \times 7^2 \times h
\]

Calculate \( 7^2 \):

\[
7^2 = 49
\]

Now substitute \( 49 \) into the equation:

\[
7693 = 3.14 \times 49 \times h
\]

Calculate \( 3.14 \times 49 \):

\[
3.14 \times 49 \approx 153.86
\]

Now we have:

\[
7693 = 153.86 \times h
\]

To find \( h \), divide both sides by \( 153.86 \):

\[
h = \frac{7693}{153.86} \approx 50
\]

Thus, the height of the cylinder is approximately:

\[
h \approx 50 \, \text{cm}
\]

The correct answer is:

**50 cm**