during practice, the northwood football team drinks water from a cylindrical cooler that has a radius of 6…

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.

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.

Answer

Explanation:

Step1: Calculate volume of cylindrical cooler

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 6$ inches and $h=20$ inches. So $V_{cylinder}=\pi\times6^{2}\times20=\pi\times36\times20 = 720\pi$ cubic - inches.

Step2: Calculate volume of conical cup

The volume formula for a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Given $r=\frac{4.4}{2}=2.2$ inches and $h = 5.5$ inches. So $V_{cone}=\frac{1}{3}\pi\times(2.2)^{2}\times5.5=\frac{1}{3}\pi\times4.84\times5.5=\frac{26.62\pi}{3}$ cubic - inches.

Step3: Calculate number of cups

The number of cups $n=\frac{V_{cylinder}}{V_{cone}}=\frac{720\pi}{\frac{26.62\pi}{3}}=\frac{720\pi\times3}{26.62\pi}=\frac{2160}{26.62}\approx81$. The total number of cups needed for 38 players with 2 cups each is $38\times2 = 76$ cups. Since $81>76$, there is enough water.

Answer:

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