Question

Taylor has a punch bowl shaped like a cylinder, with a diameter of 22 inches and a height of 20 inches. She pours 8.25 gallons of punch into the bowl. How far from the top of the punch bowl is to the top of the punch?(note:1 gallon=231 cubic inches) *please show all steps)

Answer 1

Explanation

We are given the following information:

`\begin{gathered} Diameter=22inches \\ Height=20inches \\ Volume\text{ }of\text{ }punch=8.25gallons \end{gathered}`

We are required to determine how far from the top of the punch bowl is to the top of the punch. This can be calculated as:

`Distance=Height\text{ }of\text{ }cylinder-Height\text{ }of\text{ }punch`

Therefore, the height of the punch in the cylinder can be calculated as:

`\begin{gathered} Volume=\pi r^2h \\ where \\ V=8.25gallons=8.25*231=1905.75\text{ }inches^3 \\ r=(D)/(2)=(22)/(2)=11\text{ }inches \\ \pi=3.14 \\ \therefore1905.75=3.14*11^2* h \\ 1905.75=3.14*121* h \\ h=(1905.75)/(3.14*121) \\ h\approx5inches \end{gathered}`

So, the distance from the top of the punch bowl is to the top of the punch is:

`\begin{gathered} Distance=Height\text{ }of\text{ }cylinder-Height\text{ }of\text{ }punch \\ Distance=20-5 \\ Distance=15inches \end{gathered}`

Hence, the answer is approximately 15 inches.