Question

. The dimensions of a rectangular prism are 9 inches wide by 18 inches long by 2 feet tall. What is the volume of the prism in cubic feet? (A) \(2.25\) (B) \(8.75\) (C) 36 (D) 324

Short answer

The volume of the rectangular prism is \(2.25\) cubic feet (Option A).

Step-by-step solution

Convert dimensions from inches to feet

To convert the dimensions of the prism from inches to feet, we need to remember that there are 12 inches in 1 foot. We will divide the dimensions given in inches by 12. 9 inches = 9/12 feet = 0.75 feet 18 inches = 18/12 feet = 1.5 feet The dimensions of the prism in feet are 0.75 feet wide by 1.5 feet long by 2 feet tall.

Calculate the volume of the prism

Now that we have the dimensions in feet, we can calculate the volume by multiplying the length, width, and height together. Volume = Length × Width × Height = 0.75 feet × 1.5 feet × 2 feet = 2.25 cubic feet.

Match the answer to the options provided

The volume of the prism is 2.25 cubic feet. Looking at the answer choices, we see that option (A) is the correct answer. The volume of the rectangular prism is 2.25 cubic feet (Option A).

Key concepts

Rectangular Prism Volume

A rectangular prism is a three-dimensional object with six faces, all in the shape of rectangles. To find the volume of such a prism, you need to find the product of its three dimensions: length, width, and height. Each dimension measures a different aspect of the prism:

• Length: The longest side of the base rectangle.
• Width: The shorter side of the base rectangle.
• Height: The measure extending from the base to the top face of the prism.

The volume (V) of a rectangular prism is calculated with the formula:\[ V = \text{Length} \times \text{Width} \times \text{Height} \]In the original problem, when each dimension is converted to feet, the calculation becomes:\[ V = 0.75 \text{ ft} \times 1.5 \text{ ft} \times 2 \text{ ft} = 2.25 \text{ cubic feet} \]Thus, understanding how to find volume helps in determining how much space the prism occupies.

Unit Conversion

Unit conversion is a crucial skill in geometry and beyond, especially when you need to work with different measurement systems. Often, dimensions might be given in a unit that doesn't match the desired result or context, like converting inches to feet in this exercise.
In our example, the width and length were originally given in inches but needed conversion to feet to match the height and find the volume in cubic feet. The conversion is straightforward:

• Remember, there are 12 inches in 1 foot.
• To convert inches to feet, divide the number of inches by 12.

Using this method:

• 9 inches becomes \( \frac{9}{12} = 0.75 \) feet.
• 18 inches becomes \( \frac{18}{12} = 1.5 \) feet.

With these converted measurements, you can then proceed to calculate volume in cubic feet, ensuring all dimensions are in the same unit.

Measurement in Feet

Feet is a common unit of measurement within the imperial system, especially prevalent in the United States. It's essential to be comfortable using and converting measurements to feet since it's frequently used in building and architecture measurements.
When solving problems that involve dimensions, it's crucial to have all measurements in the same unit. For instance, when dealing with volume, like in this exercise, measurements in feet provide consistency and ensure accurate computations.

• Feet are substantial enough to measure room dimensions and sizable objects, making them practical for real-world applications.
• Always ensure you're converting other units such as inches into feet before performing further calculations to avoid errors.

By having all three dimensions in feet for the volume calculation, you ensure continuity and correctness in the conversion process, leading to the correct determination of the prism's volume.