https://file.aiquickdraw.com/mathbot/file/1727408234009v1qfwc9p.jpg

The question asks to **calculate the capacity of a hemispherical tank** in **US gallons**, given that the tank has an **overall length (OL) of 24 feet** and a **radius of 3 feet**.

Let's clarify the problem:

1. A **hemispherical tank** means we are dealing with half of a sphere.
2. The formula for the volume \( V \) of a hemisphere is:
   \[
   V = \frac{2}{3} \pi r^3
   \]
   where \( r \) is the radius of the hemisphere.
3. Once we compute the volume in cubic feet, we can convert this to US gallons using the conversion factor:
   \[
   1 \text{ cubic foot} = 7.48 \text{ US gallons}
   \]

Now, let's solve the problem step by step:

- Radius \( r = 3 \, \text{ft} \)
- Calculate the volume of the hemisphere in cubic feet.
- Convert the volume to US gallons.

I'll calculate it for you now.The capacity of the hemispherical tank is approximately:

- **56.55 cubic feet**
- **422.98 US gallons**

Would you like any further details or clarifications?

Here are some related questions you might find useful:
1. How do you calculate the volume of a full sphere?
2. What is the formula for converting volumes in different units (e.g., liters, gallons)?
3. How does the volume change if the radius of the tank is doubled?
4. What is the difference between UK gallons and US gallons in terms of volume conversion?
5. How does the volume of a hemisphere compare to other shapes like cylinders or cones?

**Tip:** Always double-check units during volume conversions to ensure accurate results.

Calculate the capacity in US gallons of a hemispherical tank with an OL of 24 ft and a radius of 3 ft.

Learn how to calculate the capacity of a hemispherical tank with a radius of 3 ft and overall length (OL) of 24 ft. This problem involves using the formula for the volume of a hemisphere and converting cubic feet to US gallons.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation