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During practice, the Northwood football team drinks water from a cylindrical cooler that has a radius of 6 inches and a height of 20 inches. Players use conical paper cups, as shown below.
A cone has a diameter of 4.4 inches and a height of 5.5 inches.
If the water cooler is filled completely, can each of the 38 players have two full paper cups of water during practice? Explain.
No, because there is enough water in the cooler for about 3 cups total.
No, because there is enough water in the cooler for about 59 cups total.
Yes, because there is enough water in the cooler for about 81 cups total.
Yes, because there is enough water in the cooler for about 2,261 cups total.
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Compute volumes.
Cooler (cylinder): V = πr^2h = π(6^2)(20) = 720π ≈ 2261.95 in^3.
Cup (cone): radius = 2.2 in, height = 5.5 in,
V = (1/3)πr^2h = (1/3)π(2.2^2)(5.5) = (26.62/3)π ≈ 8.8733π ≈ 27.88 in^3.
Number of cups ≈ 2261.95 / 27.88 ≈ 81.14 → about 81 cups.
Players need 38 × 2 = 76 cups, and 81 > 76, so yes. Choice: "Yes, because there is enough water in the cooler for about 81 cups total."
Cooler (cylinder): V = πr^2h = π(6^2)(20) = 720π ≈ 2261.95 in^3.
Cup (cone): radius = 2.2 in, height = 5.5 in,
V = (1/3)πr^2h = (1/3)π(2.2^2)(5.5) = (26.62/3)π ≈ 8.8733π ≈ 27.88 in^3.
Number of cups ≈ 2261.95 / 27.88 ≈ 81.14 → about 81 cups.
Players need 38 × 2 = 76 cups, and 81 > 76, so yes. Choice: "Yes, because there is enough water in the cooler for about 81 cups total."
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