Cups A and B are cone shaped and have heights of $28 cm$ and $23 cm$ and openings with radii of $11 cm$ and $9 cm$ , 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 · 2017-12-26T13:39:03

Cup A will be filled upto 15.3967 cm

Volume of cone B $V_b= (1/3) pi r_2^2 h_2$

Given $r_2 = 9 cm, h_2 = 23 cm$

$V_b = (1/3) * pi * 9^2 * 23 = 1950.929 pi$ $cm^3$

Similarly Volume of cone A $V_a = (1/3) pi r_1^2 h_1$

Given $r-1 = 11 cm, h_1 = 28 cm$

$V_a = (1/3) * pi * 11^2 * 37 = 3547.9053 pi$ $cm^3$

As volume of cone A is greater than the volume of cone B, cup A will not overflow.

Volume of partly filled cone A $V_p = (1/3) pi r_1^2 h_3$

$V_p = = V_b$

$(1/3) pi * 9^2 * 23 = (1/3) * pi * 11^2 * h_3$

$h_3 = (cancel((1/3) * pi) * 9^2 * 23) / (cancel((1/3) * pi) * 11^2)$

$h_3 =( 1863) / 121 = 15.3967$ $cm$

Cups A and B are cone shaped and have heights of 28 cm28 cm and 23 cm23 cm and openings with radii of 11 cm11 cm and 9 cm9 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?