Jose is wrapping a stack of 100 coins in a paper holder. Each coin is 1/8 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 ππ.
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KennyOliver 1 year ago56 response - 0 helps
- What is being described is essentially a cylinder (like a tin can)!
- Note: for this question let's assume the paper's thickness doesn't matter
- If there's 100 coins, each being 1/8 inch thick
- The height of the cylinder must be 100 * 1/8 = 12.5 inches
- To find the area of the bottom and top of our cylinder let's first calculate 1 side:
- The area of a circle = π × r²
- area = π × (1/8)² = π/16 inches²
- two circles is just double the area: 2 * π/16 = π/8
- Now that we know the height and the area of the top + bottom
- We can now use the cylinder formula for surface area
- A = 2πrh + 2πr² (notice how we've already done 2πr² with our circles!)
- A = 2 × π × 1/8 × 12.5 + π/8
- A = (13π) / 4 = (13 × 3.14) / 4 = 10.205 inches²