What should the area of the base be? ### How to Calculate the Area of the Base of a 3-Foot Tall Chest with a Volume of 75 Cubic Feet**Problem Statement**: You are building a 3-foot tall chest. You want the volume to be 75 cubic feet. What should the area of the base be?**Volume Formula**:The volume $ V $ of a rectangular prism (or chest) is given by:\[ V = \text{area of the base} \times \text{height} \]**Given Data**:- Height of the chest $ h = 3 $ feet- Volume $ V = 75 $ cubic feet**Step-by-Step Solution**:1. **Write down the volume formula**: \[ V = A \times h \] where $ A $ is the area of the base.2. **Substitute the known values into the equation**: \[ 75 = A \times 3 \]3. **Solve for the area of the base $ A $**: \[ A = \frac{75}{3} \] \[ A = 25 \]Therefore, **the area of the base should be** $ 25 $ square feet.**Explanation of Diagram**:The diagram shows a rectangular prism representing the chest. It indicates the height is 3 feet and the volume is 75 cubic feet. To find the area of the base, one would use the given formula and values as shown in the solution above.

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You are building a 3-foot tall chest. You want the volume to be 75 cubic feet. What should the area of the base 3 ft

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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What should the area of the base be?

### How to Calculate the Area of the Base of a 3-Foot Tall Chest with a Volume of 75 Cubic Feet

**Problem Statement**:
You are building a 3-foot tall chest. You want the volume to be 75 cubic feet. What should the area of the base be?

**Volume Formula**:
The volume $ V $ of a rectangular prism (or chest) is given by:
\[ V = \text{area of the base} \times \text{height} \]

**Given Data**:
- Height of the chest $ h = 3 $ feet
- Volume $ V = 75 $ cubic feet

**Step-by-Step Solution**:

1. **Write down the volume formula**:
\[ V = A \times h \]
where $ A $ is the area of the base.

2. **Substitute the known values into the equation**:
\[ 75 = A \times 3 \]

3. **Solve for the area of the base $ A $**:
\[ A = \frac{75}{3} \]
\[ A = 25 \]

Therefore, **the area of the base should be** $ 25 $ square feet.

**Explanation of Diagram**:
The diagram shows a rectangular prism representing the chest. It indicates the height is 3 feet and the volume is 75 cubic feet. To find the area of the base, one would use the given formula and values as shown in the solution above.

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