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# If all the ice melted in the cup, would it overflow?

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A snowcone with a radius of 4 cm is sold in a cone-shaped paper cup with a height of 12 cm and an opening 6 cm wide. If all the ice melted in the cup, would it overflow?

Nov 27, 2018

#1
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No.

Nov 27, 2018
#2
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Volume of sphere: $$\frac{4}{3}\pi r^3$$    r = 4cm

Volume of cone:  $$\frac{1}{3}\pi r^2h$$   r = 3cm   h = 12cm

Plug in the numbers to see which is larger.

Nov 27, 2018