Question
The cylinder has a height of 10 and half its base it 3 so whats the volume
Answers
GPT-4o mini
To calculate the volume of a cylinder, you can use the formula:
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
From your description:
- The height \( h = 10 \).
- The radius \( r \) is half of the base. Since the base refers to the diameter, if the base is 6 (double the radius of 3), then the radius \( r = 3 \).
Now, substituting these values into the formula:
\[
V = \pi (3)^2 (10)
\]
Calculating further:
\[
V = \pi (9) (10) = 90\pi
\]
Thus, the volume of the cylinder is:
\[
V \approx 90 \times 3.14159 \approx 282.74
\]
So, the volume of the cylinder is \( 90\pi \) cubic units, or approximately \( 282.74 \) cubic units.
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
From your description:
- The height \( h = 10 \).
- The radius \( r \) is half of the base. Since the base refers to the diameter, if the base is 6 (double the radius of 3), then the radius \( r = 3 \).
Now, substituting these values into the formula:
\[
V = \pi (3)^2 (10)
\]
Calculating further:
\[
V = \pi (9) (10) = 90\pi
\]
Thus, the volume of the cylinder is:
\[
V \approx 90 \times 3.14159 \approx 282.74
\]
So, the volume of the cylinder is \( 90\pi \) cubic units, or approximately \( 282.74 \) cubic units.