Question
For the hot tub to run properly, the water needs to be 33 inches deep. What geometric shape can be used to estimate the number of cubic feet of water that is needed to make the hot tub ready for use?
A.
a sphere with a radius of 3.5 feet
B.
a sphere with a radius of 16.5 inches
C.
a rectangular prism with dimensions of 7 ft × 7 ft × 33 ft
D.
a rectangular prism with dimensions of 7 ft × 7 ft × 2.75 ft
A.
a sphere with a radius of 3.5 feet
B.
a sphere with a radius of 16.5 inches
C.
a rectangular prism with dimensions of 7 ft × 7 ft × 33 ft
D.
a rectangular prism with dimensions of 7 ft × 7 ft × 2.75 ft
Answers
Answered by
GPT-4o mini
To determine which geometric shape can be used to estimate the number of cubic feet of water needed for the hot tub, we need to analyze the given options in relation to the depth requirement of 33 inches.
First, we need to convert the required depth from inches to feet since the other dimensions in the options are in feet.
33 inches is equivalent to:
\[
\frac{33}{12} = 2.75 \text{ feet}
\]
Now, let’s evaluate each option based on the depth of water required:
A. A sphere with a radius of 3.5 feet:
- A sphere’s volume is calculated using \(\frac{4}{3} \pi r^3\), and it doesn’t fit the shape of a hot tub that would hold water to a specific depth.
B. A sphere with a radius of 16.5 inches:
- Similar to option A, a sphere does not represent a hot tub shape, and the volume calculation would not allow for a specified depth appropriate to hold water.
C. A rectangular prism with dimensions of 7 ft × 7 ft × 33 ft:
- The volume for this prism would be \(7 \times 7 \times 33\), which equates to 1,617 cubic feet. However, the height is given as 33 ft instead of 2.75 ft required for the hot tub.
D. A rectangular prism with dimensions of 7 ft × 7 ft × 2.75 ft:
- This option fits the requirement perfectly since it corresponds to the correct depth. The volume calculation would be \(7 \times 7 \times 2.75\) which results in a more accurate estimate for the water needed.
Thus, the best answer is:
**D. a rectangular prism with dimensions of 7 ft × 7 ft × 2.75 ft**.
First, we need to convert the required depth from inches to feet since the other dimensions in the options are in feet.
33 inches is equivalent to:
\[
\frac{33}{12} = 2.75 \text{ feet}
\]
Now, let’s evaluate each option based on the depth of water required:
A. A sphere with a radius of 3.5 feet:
- A sphere’s volume is calculated using \(\frac{4}{3} \pi r^3\), and it doesn’t fit the shape of a hot tub that would hold water to a specific depth.
B. A sphere with a radius of 16.5 inches:
- Similar to option A, a sphere does not represent a hot tub shape, and the volume calculation would not allow for a specified depth appropriate to hold water.
C. A rectangular prism with dimensions of 7 ft × 7 ft × 33 ft:
- The volume for this prism would be \(7 \times 7 \times 33\), which equates to 1,617 cubic feet. However, the height is given as 33 ft instead of 2.75 ft required for the hot tub.
D. A rectangular prism with dimensions of 7 ft × 7 ft × 2.75 ft:
- This option fits the requirement perfectly since it corresponds to the correct depth. The volume calculation would be \(7 \times 7 \times 2.75\) which results in a more accurate estimate for the water needed.
Thus, the best answer is:
**D. a rectangular prism with dimensions of 7 ft × 7 ft × 2.75 ft**.