Cups A and B are cone shaped and have heights of $32 cm$ and $27 cm$ and openings with radii of $12 cm$ and $13 cm$ , 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 · 2018-01-22T12:26:47

$31.9$ cm high of cup A will be filled.

Height and radius of cup A is $h_a=32 cm , r_a=12$ cm

Volume om cone is $1/3*pi*r^2*h :.V_a=1/3*pi*12^2*32$ or

$V_a= 4825.49$ cubic cm.

Height and radius of cup B is $h_b=27 cm , r_b=13$ cm

$:.V_b=1/3*pi*13^2*27 or V_b= 4778.36$ cubic cm.

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

The ratio of radius and hight of cup A is

$r/h=12/32 =3/8$ . The ratio of radius and hight of water cone

is $r_w/h_w=3/8 or r_w=(3*h_w)/8$

. The volume of water cone is $V_w=4778.36$ cubic cm.

$:.1/3*pi*r_w^2*h_w =4778.36$ or

$1/3*pi*((3*h_w)/8)^2*h_w =4778.36$ or

$h_w^3= (4778.36*64)/(3*pi)~~32447.9835$ or

$h_w= root(3)32447.9835 ~~ 31.90(2dp)$ cm

$31.9$ cm high of cup A will be filled [Ans]

Cups A and B are cone shaped and have heights of 32 cm32 cm and 27 cm27 cm and openings with radii of 12 cm12 cm and 13 cm13 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?