https://file.aiquickdraw.com/mathbot/file/1727407195673nonmzh26.jpg

This problem involves calculating the length of a cylindrical pipe with a known diameter, given that it needs to hold 350 US gallons of water. To solve this, we need to use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

where:
- \(V\) is the volume,
- \(r\) is the radius of the pipe (half the diameter),
- \(h\) is the height (length) of the pipe.

### Step 1: Convert diameter to radius
The diameter is given as 10 inches, so the radius \(r\) is:

\[
r = \frac{10}{2} = 5 \text{ inches}.
\]

### Step 2: Convert the volume from gallons to cubic inches
There are 231 cubic inches in a US gallon, so the total volume in cubic inches is:

\[
V = 350 \times 231 = 80,850 \text{ cubic inches}.
\]

### Step 3: Solve for the height (length) of the pipe
We rearrange the volume formula to solve for \(h\):

\[
h = \frac{V}{\pi r^2}.
\]

Substituting the values:

\[
h = \frac{80,850}{\pi (5)^2} = \frac{80,850}{\pi \times 25} = \frac{80,850}{78.54} \approx 1029.5 \text{ inches}.
\]

### Step 4: Convert the height to feet and inches
To convert 1029.5 inches to feet and inches:
- Divide by 12 to get feet: 
  \[
  \frac{1029.5}{12} \approx 85.79 \text{ feet}.
  \]
- The whole number part is 85 feet, and to get the inches:
  \[
  0.79 \times 12 \approx 9.5 \text{ inches}.
  \]

### Final Answer:
The pipe must be approximately **85 feet 9.5 inches long**. Among the options, **(b) 85' 6 3/4"** is the closest, so this is the most reasonable answer.

---

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:

1. How would the length change if the pipe diameter was increased to 12 inches?
2. How would you solve the same problem using metric units?
3. What happens to the volume if the pipe length is doubled?
4. How many gallons would a pipe 100 feet long and 12 inches in diameter hold?
5. What is the impact of using a different material, like a flexible pipe, on such calculations?

**Tip:** Always ensure units are consistent when performing volume and length calculations. Converting between systems early helps avoid mistakes later.

A pipe with a diameter of 10 inches is required to hold 350 US gallons. How long must the pipe be?

Learn how to calculate the length of a cylindrical pipe with a 10-inch diameter to hold 350 US gallons. This problem involves the cylinder volume formula and unit conversions. Suitable for high school students in grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation