# math

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Two spherical cantaloupes of the same kind are sold at a fruit and vegetable stand. The circumference of one is 60 cm and that of the other is 50 cm. The larger melon is 1 1/2 times as expensive as the smaller. Which melon is the better buy and why?

change C to radius. C=2PI r
r= C/2PI
Now volume is 4/3 PI r^3

• math -

ratio of circumference: 60/50 = 1.2
ratio of volumes: 1.2^3 = 1.728
ratio of costs: 1.5

so, since volume has gone up more than cost, the larger is a better buy.

Of course, the thickness of the rind will also be a factor. Good luck - gotta buy it before you can cut it open.

Extra credit: what rind thickness (as a % of diameter) will make them equal value?

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