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

39.25 cm
39.25 cm

50 cm
50 cm

12.5 cm
12.5 cm

175 cm

Answer 1

To find the height of a right circular cylinder, you can use the formula for the volume of a cylinder:

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

Where:
- \( V \) is the volume,
- \( \pi \) is a constant (approximately 3.14 in this case),
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

First, we need to find the radius of the cylinder. Given that the diameter is 14 cm, the radius \( r \) is:

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

Now, we can substitute the values into the volume formula. We know the volume \( V = 7693 \text{ cm}^3 \):

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

Calculating \( 7^2 \):

\[
7^2 = 49
\]

Now substitute that back into the equation:

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

Calculate \( 3.14 \times 49 \):

\[
3.14 \times 49 = 153.86
\]

So the equation now looks like this:

\[
7693 = 153.86 \times h
\]

Now, solve for \( h \):

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

Thus, the height of the cylinder is:

\[
\boxed{50 \text{ cm}}
\]