Question

Swim Fun is building a new swimming pool in the shape of an upside-down rectangular pyramid. The deepest point in the middle is 12 feet deep and the length of the pool is 25 feet. The pool can hold 1,800 cubic feet of water. How wide is the pool?(1 point)
Responses

100 feet
100 feet

300 feet
300 feet

18 feet
18 feet

600 feet

Answer 1

To determine the width of the swimming pool, we can use the volume formula for the shape of a prism (which in this case is an upside-down rectangular pyramid).

The volume \( V \) of a pyramid is given by the formula:

\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

In this case, the base area of the pool is the area of the rectangle at the top of the pyramid, which we will denote as \( A \), and the height of the pyramid (which is the depth of the pool at its deepest point) is 12 feet.

Given that the volume of the pool is 1,800 cubic feet, we can set up the equation:

\[
1800 = \frac{1}{3} \times A \times 12
\]

Solving for \( A \):

Multiply both sides by 3:

\[
5400 = A \times 12
\]

Now divide by 12:

\[
A = \frac{5400}{12} = 450
\]

Now we need to find the dimensions of the pool. Since the pool is shaped like a rectangle, we know:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Given that the length is 25 feet:

\[
450 = 25 \times \text{Width}
\]

Now solve for the width:

\[
\text{Width} = \frac{450}{25} = 18
\]

Therefore, the width of the pool is **18 feet**.

Answer 2

The volume formula for a prism is V=Bh
𝑉
=
𝐵
ℎ
. What takes the place of B
𝐵
in the formula when finding the volume of a cylinder?(1 point)