Question
A storage container for oil is in the shape of a cylinder with a diameter of 8 ft and a height of 16 ft. Which measurement is closest to the volume of the storage container in cubic feet?
Responses
A 804.25 ft³804.25 ft³
B 33,216.99 ft³33,216.99 ft³
C 1,608.50 ft³1,608.50 ft³
D 402.12 ft³
Responses
A 804.25 ft³804.25 ft³
B 33,216.99 ft³33,216.99 ft³
C 1,608.50 ft³1,608.50 ft³
D 402.12 ft³
Answers
GPT-4o mini
To find the volume of a cylindrical storage container, we use the formula:
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
1. **Determine the radius**: Since the diameter is 8 ft, the radius \( r \) is half of that:
\[
r = \frac{8}{2} = 4 \text{ ft}
\]
2. **Height**: The height \( h \) is given as 16 ft.
3. **Calculate the volume**:
\[
V = \pi (4)^2 (16)
\]
Calculating \( (4)^2 \):
\[
(4)^2 = 16
\]
Now substitute back into the volume formula:
\[
V = \pi (16)(16) = \pi (256)
\]
We use the approximation \( \pi \approx 3.14159 \):
\[
V \approx 3.14159 \times 256 \approx 804.25
\]
Thus, the volume of the storage container is approximately \( 804.25 \) cubic feet.
The closest measurement to the volume of the storage container is:
**A 804.25 ft³**
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
1. **Determine the radius**: Since the diameter is 8 ft, the radius \( r \) is half of that:
\[
r = \frac{8}{2} = 4 \text{ ft}
\]
2. **Height**: The height \( h \) is given as 16 ft.
3. **Calculate the volume**:
\[
V = \pi (4)^2 (16)
\]
Calculating \( (4)^2 \):
\[
(4)^2 = 16
\]
Now substitute back into the volume formula:
\[
V = \pi (16)(16) = \pi (256)
\]
We use the approximation \( \pi \approx 3.14159 \):
\[
V \approx 3.14159 \times 256 \approx 804.25
\]
Thus, the volume of the storage container is approximately \( 804.25 \) cubic feet.
The closest measurement to the volume of the storage container is:
**A 804.25 ft³**