Questions: A sheet of custom-size copy paper measures 5.5 in. by 14 in. If a ream (500 sheets) of this paper has a volume of 154 in.^3, how thick is the ream? The ream is thick. (Simplify your answer. Type an integer or a fraction.)

$A sheet of custom-size copy paper measures 5.5 in. by 14 in. If a ream (500 sheets) of this paper has a volume of 154 in.^3, how thick is the ream? The ream is thick. (Simplify your answer. Type an integer or a fraction.)$

Transcript text: A sheet of custom-size copy paper measures 5.5 in. by 14 in . If a ream ( 500 sheets) of this paper has a volume of 154 in. $^{3}$, how thick is the ream? The ream is $\square$ $\square$ thick. (Simplify your answer. Type an integer or a friction.)

Solution

Solution Steps

To find the thickness of the ream, we need to calculate the height of the stack of 500 sheets of paper. We know the volume of the ream and the area of one sheet. By dividing the volume by the area of one sheet, we can find the thickness of the ream.

Calculate the area of one sheet of paper using its dimensions.
Use the volume of the ream to find the thickness by dividing the volume by the area of one sheet.

Step 1: Calculate the Area of One Sheet

To find the area of one sheet of paper, we multiply its width by its length. Given the dimensions:

Width = 5.5 inches
Length = 14 inches

The area $ A $ of one sheet is calculated as: \[ A = \text{width} \times \text{length} = 5.5 \times 14 = 77.0 \, \text{in}^2 \]

Step 2: Calculate the Thickness of the Ream

The volume of the ream is given as 154 cubic inches. To find the thickness $ T $ of the ream, we divide the volume of the ream by the area of one sheet: \[ T = \frac{\text{Volume of ream}}{\text{Area of one sheet}} = \frac{154}{77.0} = 2.0 \, \text{inches} \]