Cups A and B are cone shaped and have heights of 28 cm28cm and 23 cm23cm and openings with radii of 11 cm11cm and 9 cm9cm, 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?

1 Answer
Dec 26, 2017

Cup A will be filled upto 15.3967 cm

Explanation:

Volume of cone B V_b= (1/3) pi r_2^2 h_2Vb=(13)πr22h2

Given r_2 = 9 cm, h_2 = 23 cmr2=9cm,h2=23cm

V_b = (1/3) * pi * 9^2 * 23 = 1950.929 piVb=(13)π9223=1950.929π cm^3cm3

Similarly Volume of cone A V_a = (1/3) pi r_1^2 h_1Va=(13)πr21h1

Given r-1 = 11 cm, h_1 = 28 cmr1=11cm,h1=28cm

V_a = (1/3) * pi * 11^2 * 37 = 3547.9053 piVa=(13)π11237=3547.9053π cm^3cm3

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_3Vp=(13)πr21h3

V_p = = V_bVp==Vb

(1/3) pi * 9^2 * 23 = (1/3) * pi * 11^2 * h_3(13)π9223=(13)π112h3

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

h_3 =( 1863) / 121 = 15.3967 cm