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Chapter 2: Problem 107

The dimensions of a rectangular box are given to be \(10.2 \mathrm{~cm} \times 43.7 \mathrm{~cm} \times 9.56 \times 10^{2} \mathrm{~mm}\). What is its volume in liters? Be careful! The units are not all the same.

Short Answer

Expert verified
The volume of the rectangular box is approximately 44.322 liters.

Step by step solution

01

Convert all units to the same unit

First, we need to convert all dimensions to the same unit. In this case, let's convert everything to centimeters. Note that 1 cm = 10 mm, so we can convert the given 9.56 x 10^2 mm dimension to centimeters by dividing by 10. \(9.56 \times 10^{2} \mathrm{~mm} = 9.56 \times 10^{2} \frac{\mathrm{cm}}{10\mathrm{mm}} = 95.6 \mathrm{~cm}\) Now, all three dimensions are in centimeters: Length = 10.2 cm Width = 43.7 cm Height = 95.6 cm
02

Calculate the volume of the box

Now that all of the dimensions are in centimeters, we can find the volume of the rectangular box using the formula for the volume of a rectangular box (Volume = Length × Width × Height): Volume = 10.2 cm × 43.7 cm × 95.6 cm To find the volume, multiply all three dimensions: Volume = 44322.384 cm³
03

Convert the volume to liters

Now, we need to convert the volume from cubic centimeters (cm³) to liters. We know that 1 liter = 1,000 cm³. To convert the volume to liters, we will divide the volume in cm³ by 1,000: Volume = 44322.384 cm³ × \(\frac{1 \mathrm{~L}}{1000 \mathrm{~cm^3}}\) Volume = 44.322384 liters
04

Provide the final answer

The volume of the rectangular box is approximately 44.322 liters.

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