Cups A and B are cone shaped and have heights of #32 cm# and #21 cm# and openings with radii of #13 cm# and #11 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
Jun 28, 2016

cup B contents when poured into cup A will not cause overflow. cup A will be filled up #15.0355 Cm#

Explanation:

Volume of cone is #1/3*pi*r^2*h# where r is radius and h is height.

Cup A:

Given #r = 13# and #h = 32#.

Volume of cup A is #1/3*pi*13^2*32 =# #5663.24 Cm^3#

Cup B:

Given #r = 11# and #h = 21#.

Volume of cup B is #1/3*pi*11^2*21 =# #2660.91 Cm^3#

As volume of cup B is less than cup A, when the full contents of cup B are poured into cup A, it will not overflow.

The filled portion in cup A is also in the form of a cone. To determine how high it is, assume height=h and radius = 13 for the filled cone part.

Volume = #1/3*pi*13^2*h# = #2660.91 Cm^3#

#h = 2660.91/(1/3*13^2*pi) = 15.0355 Cm#