Cups A and B are cone shaped and have heights of $27 cm$ and $24 cm$ and openings with radii of $7 cm$ and $14 cm$ , 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 · 2018-08-08T11:35:29

Since volume of contents in cup A $(1385.44)$ c.cm is less than that of cup B $(4926.02)$ c.cm , cup A will overflow.

Height and radius of cup A is $h_a=27$ cm , $r_a=7$ cm

Volume of cone is $1/3*pi*r^2*h :.V_a=1/3*pi*7^2*27$ or

$V_a ~~ 1385.44$ cubic cm.

Height and radius of cup B is $h_b=24$ cm, $r_b=14$ cm

$:.V_b=1/3*pi*14^2*24 or V_b ~~ 4926.02$ cubic cm.

Since $V_a < V_b$ , the content will overflow. [Ans]

Cups A and B are cone shaped and have heights of 27 cm27 cm and 24 cm24 cm and openings with radii of 7 cm7 cm and 14 cm14 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?