Cups A and B are cone shaped and have heights of $34 cm$ and $27 cm$ and openings with radii of $11 cm$ and $5 cm$ , 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 · 2018-06-12T06:02:28

Cup A will not overflow. It will be filled up to $color(violet)(5.58 cm)$ height

Cone A $r_a = 11 cm, h_a = 34 cm$

Cone B $r_b = 5 cm, h_b = 27 cm$

Volume of Cone A $V_a = (1/3) pi (r_a)^2 h_a$

$V_a = (1/3) pi * 11^2 * 34 = 4308.17 cm^3$

Volume of Cone A $V_b = (1/3) pi (r_b)^2 h_b$

$V_a = (1/3) pi * 5^2 * 27 = 706.86 cm^3$

Since $V_b < V_a$ , it will not overflow.

$(1/3) pi (r_a)^2 * h = V_b = 225 pi$

$h = (3 * 225 * pi) / (pi * 11^2) = 5.58 cm$

Cups A and B are cone shaped and have heights of 34 cm34 cm and 27 cm27 cm and openings with radii of 11 cm11 cm and 5 cm5 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?