Cups A and B are cone shaped and have heights of #35 cm# and #21 cm# and openings with radii of #12 cm# and #18 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

1 Answer
BDT Stu.
Feb 12, 2018

Cup B will be filled 19cm high

Explanation:

Find the volume of each cup using the formula #V=πr^2h/ 3#.

Leave the answers in terms of #pi# so that the answer does not get rounded prematurely.

If Cup A is filled with water to the brim and carried to Cup B, then Cup B will not overflow, but the shape that the water will create will be a similar shape to the cup because the frustum of the cone at any point is similar to the cone itself. So find the volume scale factor by dividing the volume of Cup B by Cup A. To find the linear scale factor just cube root it. The divided the height of Cup B by the linear scale factor to find out how high the water goes.

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