Cups A and B are cone shaped and have heights of $32 cm$ and $15 cm$ and openings with radii of $9 cm$ and $3 cm$ , 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?

Question

1948 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-26T01:47:14

Cup A will not overflow

See below

The formula for the volume of a cone is $V=1/3*pi*r^2*h$

$V_A=1/3*pi*9^2*32" "=V_A=864pi" "=272.96cm^3$

$V_B=1/3*pi*3^2*15" "=V_A=45pi" "=141.30cm^3$

If cup B is full and its contents are poured into cup A, cup A will not overflow it will be $141.30/2712.96" "=0.052" "=5.2 %$

Cups A and B are cone shaped and have heights of 32 cm32 cm and 15 cm15 cm and openings with radii of 9 cm9 cm and 3 cm3 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?