Cups A and B are cone shaped and have heights of $29 cm$ and $28 cm$ and openings with radii of $7 cm$ and $12 cm$ , 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?

Question

1459 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-19T10:47:27

Since $V_B > V_B$ , cup A will overflow.

enter image source here

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

$r_A = 7cm, h_A = 29cm, r_B = 12 cm, h_B = 28cm$

$V_A = (1/3) pi 7^2 * 29 = 1488.07$ $cm^3$

$V_B = (1/3) pi 12^2 * 28 = 4222.3$ $cm^3$

Since $V_B > V_B$ , cup A will overflow.

Cups A and B are cone shaped and have heights of 29 cm29 cm and 28 cm28 cm and openings with radii of 7 cm7 cm and 12 cm12 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?