Jose is wrapping a stack of 100 coins in a paper holder. Each coin is 18 inch thick and has a diameter of
1 inch. How many square inches of paper will Jose need to cover the stack of coins? Use 3.14 for π. Enter your answer in the box.
Interesting that this post has the same typo as it had back in 2017
https://www.jiskha.com/questions/1586870/Jose-is-wrapping-a-stack-of-100-coins-in-a-paper-holder-Each-coin-is-18-inch-thick
To find the surface area of the stack of coins, we need to determine the area of the top and bottom surfaces, as well as the curved surface.
1. Finding the area of the top and bottom surfaces:
Since the coins have a diameter of 1 inch, the radius (r) of each coin is 1/2 inch. The area of a circle is given by the formula A = πr^2. So, the area of the top and bottom surfaces of one coin is:
A = π(1/2)^2 = π/4 square inches.
There are 100 coins, so the total area of the top and bottom surfaces of all the coins is:
Total area = 100 * (π/4) = 25π square inches.
2. Finding the curved surface area:
The curved surface area forms a shape similar to a cylinder. To find the curved surface area of this cylinder, we need to find its height (h).
The thickness of each coin is given as 18 inches, and there are 100 coins. So, the height (h) of the stack of coins is:
h = 18 * 100 = 1800 inches.
The curved surface area (A) of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Substituting the values, we get:
A = 2 * 3.14 * (1/2) * 1800 = 5646 square inches (approximately).
3. Finding the total surface area:
The total surface area is the sum of the top and bottom surface areas and the curved surface area:
Total surface area = top and bottom surface area + curved surface area
Total surface area = 25π + 5646 square inches.
Now, you can calculate the total square inches of paper needed to cover the stack of coins by substituting the value of π (3.14) into the equation:
Total square inches = 25 * 3.14 + 5646 = <your answer> square inches.
Performing the calculation, we get the total square inches of paper needed to cover the stack of coins.