Cups A and B are cone shaped and have heights of $25 c m$ $25 cm$ and $18 c m$ $18 cm$ and openings with radii of $8 c m$ $8 cm$ and $9 c m$ $9 cm$ , 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 · 2018-06-22T12:06:24

The cup will not overflow and $24.24$ $24.24$ cm high of cup A will be filled.

Height and radius of cup A is $h_{a} = 25 c m, r_{a} = 8$ $h_a=25 cm , r_a=8$ cm

Volume of cup A is $1/3*pi*r^2*h :.V_a=1/3*pi*8^2*25$ or

$V_a~~ 1675.52$ cubic cm.

Height and radius of cup B is $h_b=18$ cm , $r_b=9$ cm

$:.V_b=1/3*pi*9^2*18 or V_b~~ 1526.81$ cubic cm

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

The ratio of radius and height of cup A is $r/h=8/25$ .

The ratio of radius and height of content cone in cup A

is $r_c/h_c=8/25 or r_c=(8*h_c)/25$

The volume of content cone is $V_c~~1526.81$ cubic cm.

$:.1/3*pi*r_c^2*h_c ~~1526.81$ or

$1/3*pi*((8*h_c)/25)^2*h_c ~~1526.81$ or

$h_c^3= (1526.81*75)/(8*pi)~~14238.24$ or

$h_w= root(3)14238.24 ~~ 24.237 (2dp)$ cm

$24.24$ cm high of cup A will be filled [Ans]

Cups A and B are cone shaped and have heights of 25 cm25cm25 cm and 18 cm18cm18 cm and openings with radii of 8 cm8cm8 cm and 9 cm9cm9 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?