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1. A garage is shaped like a rectangular prism. What is the volume of the garage? Show your work.

Ask by Hampton Wheeler. in the United States
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

To find the volume of the garage, multiply its length, width, and height. For example, if the garage is 20 feet long, 12 feet wide, and 14 feet high, the volume is \( 20 \times 12 \times 14 = 3360 \) cubic feet.

Solution

We start by recalling that the volume \( V \) of a rectangular prism is found by multiplying its length \( L \), width \( W \), and height \( H \): \[ V = L \times W \times H \] Since the problem states that the garage is shaped like a rectangular prism, you would use the above formula. For example, if the garage dimensions were given as: - Length: \( L = 20 \) feet - Width: \( W = 12 \) feet - Height: \( H = 14 \) feet then you would substitute these values into the formula: \[ V = 20 \times 12 \times 14 \] Calculating step by step: 1. Multiply the length and width: \[ 20 \times 12 = 240 \quad \text{(square feet)} \] 2. Multiply by the height: \[ 240 \times 14 = 3360 \quad \text{(cubic feet)} \] Thus, the volume of the garage would be: \[ V = 3360 \text{ cubic feet} \] If different dimensions are provided, simply substitute them into the formula \( V = L \times W \times H \) to find the volume.

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The Deep Dive

To find the volume of a garage shaped like a rectangular prism, you can use the formula: Volume = Length × Width × Height. For example, if your garage is 20 feet long, 10 feet wide, and 8 feet high, you would calculate: Volume = 20 ft × 10 ft × 8 ft = 1600 cubic feet. Now, that’s a lot of space for your car, tools, or even a cozy workspace! When calculating volume, it's easy to mix up dimensions. One common mistake is forgetting to convert units. If your measurements are in inches but you want the volume in cubic feet, make sure to convert everything correctly! Always double-check your calculations to avoid any bloopers in your volume report!

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