Cups A and B are cone shaped and have heights of $32 cm$ and $37 cm$ and openings with radii of $16 cm$ and $17 cm$ , 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 · 2016-07-12T10:56:27

If contents of cup $B$ filled fully, is poured into cup $A$ , cup $A$ will overflow.

Let $V_1$ and $V_2$ denote the volume of cups $A & B$ resp.

Let $r$ =radii, $h$ =heights.

Volume $V$ of a cone is $V=1/3pir^2h.$

Hence, $V_1=1/3*pi*16^2*32$ and, $V_2=1/3*pi*17^2*37.$

Since, $17^2>16^2, &, 37>32$ , evidently $V_2>V_1$ .

Hence, if contents of cup $B$ filled fully, is poured into cup $A$ , cup $A$ will overflow.

Cups A and B are cone shaped and have heights of 32 cm32 cm and 37 cm37 cm and openings with radii of 16 cm16 cm and 17 cm17 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?