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Answer :
Explanation
We are given the following information:
[tex]\begin{gathered} Diameter=22inches \\ Height=20inches \\ Volume\text{ }of\text{ }punch=8.25gallons \end{gathered}[/tex]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:
[tex]Distance=Height\text{ }of\text{ }cylinder-Height\text{ }of\text{ }punch[/tex]Therefore, the height of the punch in the cylinder can be calculated as:
[tex]\begin{gathered} Volume=\pi r^2h \\ where \\ V=8.25gallons=8.25\times231=1905.75\text{ }inches^3 \\ r=\frac{D}{2}=\frac{22}{2}=11\text{ }inches \\ \pi=3.14 \\ \therefore1905.75=3.14\times11^2\times h \\ 1905.75=3.14\times121\times h \\ h=\frac{1905.75}{3.14\times121} \\ h\approx5inches \end{gathered}[/tex]So, the distance from the top of the punch bowl is to the top of the punch is:
[tex]\begin{gathered} Distance=Height\text{ }of\text{ }cylinder-Height\text{ }of\text{ }punch \\ Distance=20-5 \\ Distance=15inches \end{gathered}[/tex]Hence, the answer is approximately 15 inches.
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