Cups A and B are cone shaped and have heights of $32 cm$ and $12 cm$ and openings with radii of $5 cm$ and $8 cm$ , 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 · 2016-02-22T05:25:19

When cup B is full and its contents are poured into cup A, cup A will not overflow. It will be filled up to a height of $30.72$ cm

Volume of a cone whose radius is $r$ and height is $h$ is given by $1/3pir^2h$ .

Hence volume of Cup A is $1/3pi5^2*32$ = $(25*32)/3pi$ = $800/3pi$
and volume of Cup B is $1/3pi8^(2)*12$ = $(64*12)/3pi$ = $768/3pi$ .

As volume of Cup B is less than that of A, when cup B is full and its contents are poured into cup A, cup A will not overflow.

Let Cup A be filled till height $a$ , than $1/3pi5^2*a$ = $768/3pi$

or $25a=768$ or $a=768/25= 30.72$ cm

Cups A and B are cone shaped and have heights of 32 cm32 cm and 12 cm12 cm and openings with radii of 5 cm5 cm and 8 cm8 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?