Cups A and B are cone shaped and have heights of $20 c m$ $20 cm$ and $12 c m$ $12 cm$ and openings with radii of $5 c m$ $5 cm$ and $8 c m$ $8 cm$ , 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 · 2018-03-03T05:25:13

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

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Volume of a cone $V = (\frac{1}{3}) π r^{2} h$ $V = (1/3) pi r^2 h$

Given : $r_{a} = 5 c m, r_{b} = 8 c m, h_{a} = 20 c m, h_{b} = 12 c m$ $r_a = 5 cm, r_b = 8 cm, h_a = 20 cm, h_b = 12 cm$

$V_{a} = (\frac{1}{3}) \cdot π \cdot 5^{2} \cdot 20 = 523.5988$ $V_a = (1/3) * pi * 5^2 * 20 = 523.5988$ $cc$

$V_{b} = (\frac{1}{3}) \cdot π \cdot 8^{2} \cdot 12 = 2412.7432$ $V_b = (1/3) * pi * 8^2 * 12 = 2412.7432$ $cc$

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

Cups A and B are cone shaped and have heights of 20 cm20cm20 cm and 12 cm12cm12 cm and openings with radii of 5 cm5cm5 cm and 8 cm8cm8 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?