Cups A and B are cone shaped and have heights of 35 cm and 29 cm and openings with radii of 12 cm and 16 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?

1 Answer
Aug 8, 2016

=31.42 cm

Explanation:

Volume of Cup A=pir^2(h/3) where r=12 cm and h=35 cm
=pi(12^2)(35/3)=1680pi
Volume of Cup B=pir^2(h/3) where r=16 cm and h=29 cm
=pi(16^2)(29/3)=1508pi
Since volume of B is less than volume of A it will not overflow
Now we can write
pi(12)^2(H/3)=1508pi
or
H=4524/144=31.42 cm
where H is the height of Cup A will be filled.