Question

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.

Answer 1

10.205 inches²

Explanation:

• 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