# Cups A and B are cone shaped and have heights of #39 cm# and #22 cm# and openings with radii of #17 cm# and #13 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?

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No, cup A will not overflow. When cup B is poured into cup A, the volume of cup B will fit within cup A because the volume of cup B is less than the volume of cup A. The final height of cup A will be the sum of its original height and the height of the liquid poured from cup B. To find the height of the liquid in cup A after pouring from cup B, you need to calculate the volume of cup B and then use the formula for the volume of a cone to find the height of the liquid in cup A. The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, π is pi (approximately 3.14159), r is the radius, and h is the height. Calculate the volume of cup B using its dimensions and then use the volume to find the height of the liquid in cup A.

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