Question
A cylindrical water tank has a diameter of 6 meters and a height of 9 meters. What is the maximum volume of water the tank can hold? (to nearest whole number)
Responses
A 254
254 m 3
B 509
509 m 3
C 1018
1018 m 3
D 2290
Responses
A 254
254 m 3
B 509
509 m 3
C 1018
1018 m 3
D 2290
Answers
GPT-4o mini
To calculate the maximum volume of water that a cylindrical tank can hold, we 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 of the cylinder.
1. **Calculate the radius**: The diameter of the tank is 6 meters, so the radius \( r \) is half of that:
\[
r = \frac{6}{2} = 3 \text{ meters}
\]
2. **Height of the tank**: The height \( h \) is given as 9 meters.
3. **Calculate the volume**:
\[
V = \pi (3^2)(9)
\]
\[
V = \pi (9)(9)
\]
\[
V = 81\pi
\]
4. **Use the approximation for \(\pi\)**: To find the numerical value, we can use \( \pi \approx 3.14 \):
\[
V \approx 81 \times 3.14 \approx 254.34
\]
5. **Round to the nearest whole number**:
\[
V \approx 254
\]
Thus, the maximum volume of water the tank can hold is approximately \( 254 \, m^3 \).
The correct answer is **A: 254 m³**.
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cylinder.
1. **Calculate the radius**: The diameter of the tank is 6 meters, so the radius \( r \) is half of that:
\[
r = \frac{6}{2} = 3 \text{ meters}
\]
2. **Height of the tank**: The height \( h \) is given as 9 meters.
3. **Calculate the volume**:
\[
V = \pi (3^2)(9)
\]
\[
V = \pi (9)(9)
\]
\[
V = 81\pi
\]
4. **Use the approximation for \(\pi\)**: To find the numerical value, we can use \( \pi \approx 3.14 \):
\[
V \approx 81 \times 3.14 \approx 254.34
\]
5. **Round to the nearest whole number**:
\[
V \approx 254
\]
Thus, the maximum volume of water the tank can hold is approximately \( 254 \, m^3 \).
The correct answer is **A: 254 m³**.