https://file.aiquickdraw.com/mathbot/file/17295125660783844aqb8.jpg

This problem involves finding the volume of water in a pyramidal tank with a square base, given the side length of the base and the depth of the water. We are also asked to convert the volume into gallons. Let's break it down step by step.

### Step 1: Formula for Volume of a Pyramid
The volume \( V \) of a pyramid with a square base is given by:

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

The base area \( A \) is the area of the square, which can be calculated as:

\[
A = \text{side}^2 = 11.6^2 = 134.56 \, \text{ft}^2
\]

### Step 2: Adjusting for Water Depth
Since the water does not fill the entire tank but only up to a depth of 5.725 feet, the volume of water will be a smaller pyramid with the same square base but with height (or depth of water) \( h = 5.725 \) feet. The formula for the volume of water (which forms a smaller pyramid) is:

\[
V_{\text{water}} = \frac{1}{3} \times A \times h = \frac{1}{3} \times 134.56 \times 5.725
\]

Calculating:

\[
V_{\text{water}} = \frac{1}{3} \times 134.56 \times 5.725 = \frac{1}{3} \times 770.408 = 256.803 \, \text{cubic feet}
\]

### Step 3: Converting Cubic Feet to Gallons
To convert cubic feet to gallons, use the conversion factor:

\[
1 \, \text{cubic foot} = 7.48052 \, \text{gallons}
\]

Thus, the volume in gallons is:

\[
V_{\text{gallons}} = 256.803 \times 7.48052 = 1920.03 \, \text{gallons}
\]

### Final Answer:
The amount of water in the tank is approximately **1920 gallons**.

Would you like more details or have any questions?

### Related Questions:
1. How would the result change if the depth of the water were doubled?
2. What is the total volume of the tank when it is fully filled?
3. How would the volume change if the side length of the base increased by 10%?
4. How do we calculate the surface area of this pyramid?
5. What happens to the volume if the shape of the tank is changed to a cone with the same base and height?

### Tip:
When solving geometry problems involving volumes, always verify the shape and dimensions carefully to apply the correct formula.

The pyramidal tank shown in the figure has a square base 11.6 ft. on a side and an altitude of 14.8 ft. How many gallons of water are in it when the depth of the water is 5.725 ft?

Find the volume of water in a pyramidal tank with a square base of 11.6 ft and a water depth of 5.725 ft. The problem involves calculating the volume of a pyramid and converting cubic feet to gallons. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation