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)
Answers
GPT-4o mini
To find the height of a right circular cylinder given its volume and the diameter, 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 of the base, and
- \( h \) is the height of the cylinder.
Given:
- Volume \( V = 7693 \, \text{cm}^3 \)
- Diameter = 14 cm, therefore, the radius \( r = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \, \text{cm} \)
- Use \( \pi \approx 3.14 \)
Now, we can substitute the known values into the volume formula:
\[
7693 = 3.14 \times (7^2) \times h
\]
Calculating \( 7^2 \):
\[
7^2 = 49
\]
Now, substitute that into the equation:
\[
7693 = 3.14 \times 49 \times h
\]
Calculating \( 3.14 \times 49 \):
\[
3.14 \times 49 = 153.86
\]
Now, we have:
\[
7693 = 153.86 \times h
\]
To solve for \( h \), divide both sides by 153.86:
\[
h = \frac{7693}{153.86} \approx 50.04
\]
Therefore, the height of the cylinder is approximately:
\[
\boxed{50 \, \text{cm}}
\]
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base, and
- \( h \) is the height of the cylinder.
Given:
- Volume \( V = 7693 \, \text{cm}^3 \)
- Diameter = 14 cm, therefore, the radius \( r = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \, \text{cm} \)
- Use \( \pi \approx 3.14 \)
Now, we can substitute the known values into the volume formula:
\[
7693 = 3.14 \times (7^2) \times h
\]
Calculating \( 7^2 \):
\[
7^2 = 49
\]
Now, substitute that into the equation:
\[
7693 = 3.14 \times 49 \times h
\]
Calculating \( 3.14 \times 49 \):
\[
3.14 \times 49 = 153.86
\]
Now, we have:
\[
7693 = 153.86 \times h
\]
To solve for \( h \), divide both sides by 153.86:
\[
h = \frac{7693}{153.86} \approx 50.04
\]
Therefore, the height of the cylinder is approximately:
\[
\boxed{50 \, \text{cm}}
\]