Cups A and B are cone shaped and have heights of $16 cm$ and $15 cm$ 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 · 2018-01-28T11:42:52

$11.95$ cm high of cup A will be filled.

Height and radius of cup A is $h_a=16$ cm , $r_a=6$ cm

Volume of cup is $1/3*pi*r^2*h :.V_a=1/3*pi*6^2*16$ or

$V_a ~~ 603.19$ cubic cm.

Height and radius of cup B is $h_b=15$ cm , $r_b=4$ cm

$:.V_b=1/3*pi*4^2*15 or V_b ~~ 251.33$ 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 cup A filled

with water is $r_w/h_w=6/16=3/8 or r_w=(3*h_w)/8$

The volume of water cone is $V_w=251.33$ cubic cm.

$:.1/3*pi*r_w^2*h_w =251.33$ or

$1/3*pi*((3*h_w)/8)^2*h_w =251.33$ or

$h_w^3= (251.33*64)/(3*pi)~~1706.684$ or

$h_w= root(3)1706.684 ~~ 11.95(2dp)$ cm

$11.95$ cm high of cup A will be filled [Ans]

Cups A and B are cone shaped and have heights of 16 cm16 cm and 15 cm15 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?