Question

ANSWERS GET MEDALS!!
Cory manufactures mugs in the shape of cylinders. He wants all of the mugs to have the same fixed volume. This implies that the height of a given mug will vary inversely with the square of its diameter. One of his mugs has a diameter of 4 inches and a height of 9 inches. If another mug has a diameter of 6 inches, what should its height be?

Answer 1

h = 4

Answer 2

\[h = k/d ^{2}\]
\[k = d ^{2} h = 4^{2} *9 = 144\]
\[6^{2} h = 144\]
h = 144/36 = 4 incies.

Answer 3

\[v=\frac{d^2 \pi }{4}h \]The volume of the first mug is 36 pi. So all mugs must satisfy the following equation:\[\frac{d^2 \pi }{4}h=36 \pi \]Solve the above for h when d = 6, the diameter of the second mug.\[\frac{1}{4} d^2 h \pi =36 \pi \text{, }\frac{1}{4} 6^2 h \pi =36 \pi \text{, } 9 h \pi =36 \pi \text{, }h=4 \]

Answer 4

The problem is stated in such a way that we can compute the height using only the information given there and our knowledge about variation.