Cups A and B are cone shaped and have heights of $12 cm$ and $18 cm$ and openings with radii of $6 cm$ and $4 cm$ , 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 · 2018-04-09T12:29:19

$10.48$ cm high of cup A will be filled

Height and radius of cup A is $h_a=12 cm , r_a=6$ cm

Volume om cone is $1/3*pi*r^2*h :.V_a=1/3*pi*6^2*12$ or

$V_a~~ 452.39$ cubic cm.

Height and radius of cup B is $h_b=18$ cm , $r_b=4$ cm

$:.V_b=1/3*pi*4^2*18 or V_b~~ 301.59$ cubic cm.

Since $V_a > V_b$ , the content will not overflow.

The ratio of radius and hight of cup A is

$r/h=6/12 =1/2$ . The ratio of radius and hight of water cone

is $r_w/h_w=1/2 or r_w=h_w/2$

The volume of water cone is $V_w=301.59$ cubic cm.

$:.1/3*pi*r_w^2*h_w =301.59$ or

$1/3*pi*(h_w/2)^2*h_w =301.59$ or

$h_w^3= (301.59*12)/pi~~1151.99$ or

$h_w= root(3)1151.99 ~~ 10.48 (2dp)$ cm

$10.48$ cm high of cup A will be filled [Ans]

Cups A and B are cone shaped and have heights of 12 cm12 cm and 18 cm18 cm and openings with radii of 6 cm6 cm and 4 cm4 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?