Question

cylinders
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.
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.

Explanation:

Step1: Calculate cooler volume (cylinder)

Volume formula: $V_{cylinder} = \pi r^2 h$
Substitute $r=6$, $h=20$:
$V_{cylinder} = \pi \times 6^2 \times 20 = \pi \times 36 \times 20 = 720\pi$ cubic inches

Step2: Calculate cup volume (cone)

First find cup radius: $r_{cone} = \frac{4.4}{2} = 2.2$ inches
Volume formula: $V_{cone} = \frac{1}{3}\pi r^2 h$
Substitute $r=2.2$, $h=5.5$:
$V_{cone} = \frac{1}{3} \pi \times 2.2^2 \times 5.5 = \frac{1}{3} \pi \times 4.84 \times 5.5 = \frac{26.62}{3}\pi \approx 8.873\pi$ cubic inches

Step3: Find total cups possible

Divide cooler volume by cup volume:
$\text{Total cups} = \frac{V_{cylinder}}{V_{cone}} = \frac{720\pi}{\frac{26.62}{3}\pi} = \frac{720 \times 3}{26.62} \approx 81$

Step4: Calculate required cups

38 players × 2 cups each = 76 cups

Answer:

Yes, because there is enough water in the cooler for about 81 cups total.