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Chapter 9: Problem 487

Find the volume of a rectangular room with width 12 feet, length 15 feet, and height 8 feet.

Short Answer

Expert verified
The volume of the room is 1440 cubic feet.

Step by step solution

01

Identify the dimensions

Write down the given dimensions of the room. The width is 12 feet, the length is 15 feet, and the height is 8 feet.
02

Use the volume formula for a rectangular prism

Recall that the volume of a rectangular prism (or a rectangular room) is given by the formula \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
03

Substitute the given dimensions into the formula

Substitute the values you have identified into the volume formula: \[ \text{Volume} = 15 \text{ feet} \times 12 \text{ feet} \times 8 \text{ feet} \]
04

Perform the multiplication

Multiply the dimensions to find the volume: \[ 15 \times 12 = 180 \text{ square feet} \] Next, \[ 180 \times 8 = 1440 \text{ cubic feet} \]
05

State the final answer

The volume of the rectangular room is 1440 cubic feet.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Volume Calculation
Understanding how to calculate volume is essential in geometry and everyday life. The volume of an object tells us how much space it occupies, which can be crucial for various applications.

For rectangular prisms, calculating volume is straightforward. You need three key dimensions: length, width, and height. These dimensions are multiplied together using the formula: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]

By multiplying these three values, you get the total volume in cubic units. Always ensure your dimensions are in the same measurement unit before multiplying.
Rectangular Prism
A rectangular prism is a 3-dimensional geometric shape with six faces, all of which are rectangles. Understanding this shape is key to many volume-related problems.

Here are its main characteristics:
  • It has length, width, and height.
  • Opposite faces are identical.
  • All angles are right angles.

In real life, many objects are shaped like rectangular prisms, such as rooms, boxes, and books.

For example, consider a room with a width of 12 feet, a length of 15 feet, and a height of 8 feet. This room is a rectangular prism. To find out how much space is inside, we use the volume formula mentioned above.
Multiplication in Geometry
Multiplication is a fundamental operation in geometry, especially when calculating volume. When dealing with 3-dimensional objects like rectangular prisms, multiplication helps us combine different dimensions.

To find volume:
  • Multiply the length and width to get the area of one face. For our example: \[15 \text{ feet} \times 12 \text{ feet} = 180 \text{ square feet} \]
  • Then, multiply this area by the height to get the total volume: \[180 \text{ square feet} \times 8 \text{ feet} = 1440 \text{ cubic feet} \]

This shows how important multiplication is in transforming 2-dimensional measurements into a full 3-dimensional volume, making complex concepts more manageable.

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Find the complement of a \(52^{\circ}\) angle.

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