Finding Dimensions of Cone-Shaped Drinking Cups

[animeowl]

The problem states that the height of each cup is 6 centimeters more than the radius, and the volume of each cup is 27*pi cubic centimeters. It tells me to find the dimensions of the cup.

Thanks for any help.

 

[soroban]

Hello, animeowl!

The height of each conical cup is 6 centimeters more than the radius.
The volume of each cup is \(\displaystyle 27\pi\text{ cm}^3.\)
Find the dimensions of the cup.

\(\displaystyle \text{We are told: }\:h \:=\:r+ 6\)

\(\displaystyle \text{We are expected to know the volume formula: }\:V \:=\:\frac{\pi}{3}r^2h\)

\(\displaystyle \text{We are told that: }\:V \;=\;27\pi\text{ cm}^3.\)


Can you finish the problem?