Question

A textbook is \(27 \mathrm{~cm}\) long, \(21 \mathrm{~cm}\) wide, and \(4.4 \mathrm{~cm}\) thick. What is the volume in: (a) cubic centimeters? (b) liters? (c) cubic inches?

Short answer

Volume: (a) 2494.8 cm^3, (b) 2.4948 L, (c) 152.26 in^3.

Step-by-step solution

- Find the Volume in Cubic Centimeters

To find the volume of the textbook in cubic centimeters (\text{cm}^3), use the formula for the volume of a rectangular prism: \text{Volume} = \text{length} \times \text{width} \times \text{thickness} Given values: \text{length} = 27 \text{cm}, \text{width} = 21 \text{cm}, \text{thickness} = 4.4 \text{cm} Therefore, \[ \text{Volume} = 27 \space \text{cm} \times 21 \space \text{cm} \times 4.4 \space \text{cm} = 2494.8 \space \text{cm}^3 \]

- Convert Volume to Liters

To convert cubic centimeters to liters, use the conversion factor: 1 \space \text{L} = 1000 \space \text{cm}^3 Divide the volume in cubic centimeters by 1000: \[ 2494.8 \space \text{cm}^3 \div 1000 = 2.4948 \space \text{L} \]

- Convert Volume to Cubic Inches

To convert cubic centimeters to cubic inches, use the conversion factor: 1 \space \text{in}^3 = 16.387 \space \text{cm}^3 Divide the volume in cubic centimeters by 16.387: \[ 2494.8 \space \text{cm}^3 \div 16.387 = 152.26 \space \text{in}^3 \]

Key concepts

Volume of a Rectangular Prism

The volume of a rectangular prism represents the amount of space it occupies. To find this volume, we use the formula for the volume of a rectangular prism:

• Volume = length × width × thickness

For a textbook that is 27 cm long, 21 cm wide, and 4.4 cm thick, the calculation would be: Volume = 27 cm × 21 cm × 4.4 cm = 2494.8 cm³ This result tells us how many cubic centimeters the textbook occupies.

Unit Conversion

Unit conversion is the process of changing a measurement from one unit to another while still retaining the same value. This is particularly important when working with volume because you might need to convert between different units such as cubic centimeters (cm³), liters (L), and cubic inches (in³). To convert between units, we use specific conversion factors. These factors are based on the mathematical relationships between units of measurement.

Cubic Centimeters to Liters

To convert from cubic centimeters to liters, we need to know the conversion factor:

• 1 liter (L) = 1000 cubic centimeters (cm³)

If we have a volume of 2494.8 cm³, we divide this by 1000 to convert to liters: Volume in liters = 2494.8 cm³ ÷ 1000 = 2.4948 L So, the volume of the textbook in liters is 2.4948 liters.

Cubic Centimeters to Cubic Inches

To convert from cubic centimeters to cubic inches, the conversion factor is:

• 1 cubic inch (in³) = 16.387 cubic centimeters (cm³)

Using the volume we calculated in cubic centimeters (2494.8 cm³), we divide this by 16.387: Volume in cubic inches = 2494.8 cm³ ÷ 16.387 = 152.26 in³ Therefore, the volume of the textbook in cubic inches is 152.26 cubic inches.