Crusty Circumference

Geometry Level 2

If your favorite part of the pie is the crust, then which of these two boxes of pie would you buy?

Details and Assumptions

The thickness of crust is the same regardless of pie size.
The pies are packed in identical boxes.

The two boxes have the same total amount of crust A B It's impossible to tell

1 solution

Zandra Vinegar Staff
Nov 26, 2015

Recall that $circumference = \pi \times diameter$

Say that the dimensions of the box are $X \times X$ . Then the diameter of the larger pie is $X$ and its crusty circumference is therefore $\pi \times X$ . The diameters of the pies in the box on the right would be half that, so $\frac{X}{2}$ . Therefore, the total amount of crusty circumference in that box is $4 \times \pi \times \frac{B}{2} = 2\pi \times X\$ .

Therefore, there is twice as much crusty circumference in $\fbox{box B}$ compared to box A.

I also considered the tops of the pies to be crust (pies aren't open), so I came to "the same amount" treating it as an area problem. Perhaps a clarification in the wording of the problem to only consider the edges would be helpful.

Alex Hume - 5 years, 6 months ago

Yes, please clarify it because I thought that the crust is the top of the pie, too, so I came up with the answer "the same amount"....

Andrei Stirb - 5 years, 6 months ago

The crust IS the surface. The online definition is "the pastry covering the outside of a pie or other dish."

Jay Hess - 5 years, 6 months ago

LOL, I misread the question too!

Justine Allen - 9 months, 3 weeks ago

Crusty Circumference

1 solution

1 pending report

Vote up reports you agree with