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Chapter 1: Problem 62

The dimensions of aluminum foil in a box for sale in supermarkets are \(662 / 3\) yards by 12 inches. The mass of the foil is \(0.83 \mathrm{~kg}\). If its density is \(2.70 \mathrm{~g} / \mathrm{cm}^{3}\), then what is the thickness of the foil in inches?

Short Answer

Expert verified
Answer: To find the thickness of the aluminum foil sheet, follow these steps: 1. Convert the dimensions to centimeters: Length = (662/3 yards) * (3 ft / yard) * (12 inches / ft) * (2.54 cm / inch) Width = (12 inches) * (2.54 cm / inch) 2. Find the volume of the foil using mass and density: Volume = (Mass in grams) / (Density) Volume = (830 g) / (2.70 g/cm³) 3. Calculate the thickness of the foil: Thickness = Volume / (Length * Width) 4. Convert the thickness to inches: Thickness_inches = Thickness_cm * (1 inch / 2.54 cm) Follow these steps using the given values and find the thickness of the aluminum foil sheet in inches.

Step by step solution

01

Convert given dimensions to a consistent unit system

To solve this problem, we will convert the given dimensions all to centimeters: a) Convert 662/3 yards to centimeters: Length = (662/3 yards) * (3 ft / yard) * (12 inches / ft) * (2.54 cm / inch) b) Convert 12 inches to centimeters: Width = (12 inches) * (2.54 cm / inch)
02

Find the volume of the foil using mass and density

The formula for finding volume using mass and density is: Volume = Mass / Density The mass of the foil is given in kilograms, so we need to convert it to grams: Mass = 0.83 kg * (1000 g / kg) = 830 g Now, calculate the volume of the foil: Volume = (830 g) / (2.70 g/cm³)
03

Calculate the thickness of the foil

We have the Volume, Length, and Width of the foil in centimeters. We can now set up an equation to solve for the Thickness (h), also in centimeters: Volume = (Length) * (Width) * (Thickness) Rearrange the equation to solve for Thickness: Thickness = Volume / (Length * Width) Calculate the Thickness in centimeters using the values found in Step 1 and 2: Thickness_cm = Volume / (Length * Width)
04

Convert the thickness to inches

Finally, convert the Thickness from centimeters to inches: Thickness_inches = Thickness_cm * (1 inch / 2.54 cm) Now we have the thickness of the aluminum foil in inches.

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