Another challenge: What are dimensions of the cone (with ice cream cap) and cylinder (with top and bottom) such that they will have the same volume as each other and the same surface area as each other?
EASY AS PI #8
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And this was just in my head with a bunch of background noises, nieces and nephews, but someone correct me if the answer isn't 208/9 centimeters, or 23.1111111... And I have an unfair advantage, so give the pi to someone who can explain why that's the answer. 😊
Jul 16, 2020
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#5
I may have made a mistake, but I just double checked and still got the same (different) answer. It is a whole number BTW.
Is the answer 16?
The cone's volume is 1/3*pi*36*15=180pi, the scoop is 2/3*pi*216=144pi, so the scoop and cone together is 324 pi. Thus, the volume of the soda can is 324pi=20.25*x*pi, so x=16.
ICE CREAM CONE VS SODA CAN
You have an ice cream cone and a can of soda. Assume the ice cream and the cone are solid (no air gaps inside anywhere), and that the cone is a regular cone, with the portion of ice cream sticking up from the top of the cone forming a perfect half sphere. Let's also assume for simplicity that the soda can is a perfect cylinder.
The ice cream scoop and the top of the cone both have a diameter of 12 cm, and the height of the cone (NOT including the ice cream!) is 15 cm.
If the soda can has a diameter of 9 cm., how tall would the soda can need to be in order to contain the same volume as the cone with the ice cream?