Question

A swimming pool is in the shape of a rectangular prism. The pool is 30 feet long, 16 feet wide, and 6 feet deep. James stretched a hose straight from a top corner of the pool to the bottom corner farthest away.

Question
What is the length of the hose from the top corner to the bottom corner farthest away? Enter the answer in the box. Round the answer to the nearest hundredth of a foot.

Response area with 1 text input box
feet

Answer 1

u sure

Answer 2

To find the length of the hose from the top corner of the pool to the bottom corner farthest away, we can use the Pythagorean theorem in three dimensions. The length, width, and depth of the pool can be treated as the three dimensions of a rectangular prism.

Given:
- Length of the pool (l) = 30 feet
- Width of the pool (w) = 16 feet
- Depth of the pool (d) = 6 feet

The distance \( D \) from the top corner to the farthest bottom corner can be calculated using the formula:

\[
D = \sqrt{l^2 + w^2 + d^2}
\]

Calculating step-by-step:

1. Calculate \( l^2 \):
\[
l^2 = 30^2 = 900
\]

2. Calculate \( w^2 \):
\[
w^2 = 16^2 = 256
\]

3. Calculate \( d^2 \):
\[
d^2 = 6^2 = 36
\]

4. Now sum these values:
\[
l^2 + w^2 + d^2 = 900 + 256 + 36 = 1192
\]

5. Taking the square root:
\[
D = \sqrt{1192} \approx 34.52 \text{ feet}
\]

Therefore, the length of the hose from the top corner to the bottom corner farthest away is approximately **34.52** feet.

So, the answer is:

**34.52** feet

Answer 3

Let me double-check the calculations for the diagonal length from the top corner to the bottom corner of the rectangular prism-shaped pool.

We have:
- Length (\( l \)) = 30 feet
- Width (\( w \)) = 16 feet
- Depth (\( d \)) = 6 feet

Using the formula for the diagonal in three dimensions:

\[
D = \sqrt{l^2 + w^2 + d^2}
\]

Substituting the values:

1. Calculate \( l^2 \):
\[
l^2 = 30^2 = 900
\]

2. Calculate \( w^2 \):
\[
w^2 = 16^2 = 256
\]

3. Calculate \( d^2 \):
\[
d^2 = 6^2 = 36
\]

4. Sum these values:
\[
l^2 + w^2 + d^2 = 900 + 256 + 36 = 1192
\]

5. Now, find the square root:
\[
D = \sqrt{1192}
\]

Calculating \( \sqrt{1192} \):

\[
D \approx 34.52 \text{ feet}
\]

So the initial calculation was indeed correct. The length of the hose from the top corner to the bottom corner farthest away is approximately **34.52 feet**.

If you have any specific concerns about the calculation or if there's something else you'd like to verify, please let me know!