Cups A and B are cone shaped and have heights of 29 cm29cm and 28 cm28cm and openings with radii of 7 cm7cm and 12 cm12cm, 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
Feb 19, 2018

Since V_B > V_BVB>VB, cup A will overflow.

Explanation:

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Formula for volume of a cone is given by V = (1/3) pi r^2 hV=(13)πr2h

r_A = 7cm, h_A = 29cm, r_B = 12 cm, h_B = 28cmrA=7cm,hA=29cm,rB=12cm,hB=28cm

V_A = (1/3) pi 7^2 * 29 = 1488.07VA=(13)π7229=1488.07 cm^3cm3

V_B = (1/3) pi 12^2 * 28 = 4222.3VB=(13)π12228=4222.3 cm^3cm3

Since V_B > V_BVB>VB, cup A will overflow.