Jose will need 39.25 square inches of paper to cover the stack of coins.
Given that
Jose is wrapping a stack of 100 coins in a paper holder.
Each coin is 1/8inch thick and has a diameter of 1 inch.
We have to determine
How many square inches of paper will Jose need to cover the stack of coins?
According to the question
Jose is wrapping a stack of 100 coins in a paper holder.
Each coin is 1/8inch thick and has a diameter of 1 inch.
The resulting figure of a stack of 100 coins will be a right circular cylinder.
We assume that Jose wraps around the cylinder (so it means not including the bases).
Therefore we are solving for the lateral surface area of the cylinder:
[tex]\rm Lateral \ surface \ area = 2\pi rh[/tex]
Where r is the radius and h is the height.
For the height h, we multiply the thickness of the coin 100 times.
h = 100 × 1/8 in = 12.5 inches
Solving for radius r:
r = 1 inch/2 = 0.5 inches
Substitute all the values in the formula.
[tex]\rm Lateral \ surface \ area = 2\pi rh\\
\\
Lateral \ surface \ area = = 2\times 3.14 \times 0.5 \times 12.5\\
\\
Lateral \ surface \ area = 39.25 [/tex]
Hence, Jose will need 39.25 square inches of paper to cover the stack of coins.
To know more about the Surface Area click the link given below.
https://brainly.com/question/6531179
