Quandaries and Queries


Who is asking: Student
Level: Elementary

A 2 meter diameter sphere of ice melts at 1.5 millimeters per minute. How many minutes will it take to fill up a hexagonal container measuring 1.5 meters on a side, and 0.8 meters deep?



Hi Jubi,

Find the area of the hexagon and multiply by the depth to determine the volume of water needed to fill the container. The area of the hexagon can be found using the answer I gave to a previous question by taking L = 1500 millimeters and n = 6. Make sure you convert the depth measurement to millimeters so that the volume is in cubic millimeters.

The volume of a sphere is given by

 4/3 r3

where r is the radius, so the volume of the ice sphere is initially

 4/3 10003 = cubic millimeters.

Subtract the volume of the hexagonal container to find the volume of the ice sphere that will remain when the container is full.

What is the radius of a sphere with that volume? What is its diameter? How many minutes will it take for the ice sphere to shrink to that diameter?



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