Question

Cups A and B are cone shaped and have heights of `24 cm` and `26 cm` and openings with radii of `10 cm` and `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?

Answer 1

no overflow

Explanation:

Formula for volume of a cone `V=1/3*pi*r^2*h`
volume of 1st cone `V_A=1/3*pi*10^2*24`
volume of 2nd cone `V_B=1/3*pi*9^2*26`
volume of 2nd cone `V_A/V_B=(1/3*pi*10^2*24)/(1/3*pi*9^2*26)=400/351>1`
`:.V_A>V_B`
So the cup A will not over flow when contents of full of B is poured in A