Question
Describe the volume of the cylinder with a base radius of 2.5 in. and a height of 9 in
1. π(9)2(2.5)in.3
2. π(2.5)(9)in.3
3. π(2.5)2(9)in.3
4. (2.5)(9)in.3
1. π(9)2(2.5)in.3
2. π(2.5)(9)in.3
3. π(2.5)2(9)in.3
4. (2.5)(9)in.3
Answers
GPT-4o mini
The volume \( V \) of a cylinder can be calculated using the formula:
\[
V = \pi r^2 h
\]
where \( r \) is the radius of the base, and \( h \) is the height of the cylinder.
Given that the base radius \( r = 2.5 \) inches and the height \( h = 9 \) inches, we apply these values:
1. Calculate \( r^2 \):
\[
r^2 = (2.5)^2 = 6.25
\]
2. Now, substitute \( r^2 \) and \( h \) into the volume formula:
\[
V = \pi (2.5^2)(9) = \pi (6.25)(9) = 56.25\pi \, \text{in}^3
\]
From the options given, the correct expression for the volume of the cylinder is:
**3. \(\pi(2.5^2)(9)in^3\)**.
\[
V = \pi r^2 h
\]
where \( r \) is the radius of the base, and \( h \) is the height of the cylinder.
Given that the base radius \( r = 2.5 \) inches and the height \( h = 9 \) inches, we apply these values:
1. Calculate \( r^2 \):
\[
r^2 = (2.5)^2 = 6.25
\]
2. Now, substitute \( r^2 \) and \( h \) into the volume formula:
\[
V = \pi (2.5^2)(9) = \pi (6.25)(9) = 56.25\pi \, \text{in}^3
\]
From the options given, the correct expression for the volume of the cylinder is:
**3. \(\pi(2.5^2)(9)in^3\)**.