Cups A and B are cone shaped and have heights of 20 cm20cm and 12 cm12cm and openings with radii of 5 cm5cm and 8 cm8cm, 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
Mar 3, 2018

Since volume of cup B (2412.7432) > volume of cup A (523.5988), #excess quantity of 1889.1444 cc from Cone B will overflow.

Explanation:

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Volume of a cone V = (1/3) pi r^2 hV=(13)πr2h

Given : r_a = 5 cm, r_b = 8 cm, h_a = 20 cm, h_b = 12 cmra=5cm,rb=8cm,ha=20cm,hb=12cm

V_a = (1/3) * pi * 5^2 * 20 = 523.5988Va=(13)π5220=523.5988 cc

V_b = (1/3) * pi * 8^2 * 12 = 2412.7432Vb=(13)π8212=2412.7432 cc

Since volume of cup B (2412.7432) > volume of cup A (523.5988), #excess quantity of 1889.1444 cc from Cone B will overflow.