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

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Answer 1 · 2018-02-19T10:47:27

Since $V_{B} > V_{B}$ $V_B > V_B$ , cup A will overflow.

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

$r_{A} = 7 c m, h_{A} = 29 c m, r_{B} = 12 c m, h_{B} = 28 c m$ $r_A = 7cm, h_A = 29cm, r_B = 12 cm, h_B = 28cm$

$V_{A} = (\frac{1}{3}) π 7^{2} \cdot 29 = 1488.07$ $V_A = (1/3) pi 7^2 * 29 = 1488.07$ $c m^{3}$ $cm^3$

$V_{B} = (\frac{1}{3}) π 12^{2} \cdot 28 = 4222.3$ $V_B = (1/3) pi 12^2 * 28 = 4222.3$ $c m^{3}$ $cm^3$

Since $V_{B} > V_{B}$ $V_B > V_B$ , cup A will overflow.

Cups A and B are cone shaped and have heights of 29 cm29cm29 cm and 28 cm28cm28 cm and openings with radii of 7 cm7cm7 cm and 12 cm12cm12 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?