Cups A and B are cone shaped and have heights of $38 c m$ $38 cm$ and $24 c m$ $24 cm$ and openings with radii of $12 c m$ $12 cm$ and $18 c m$ $18 cm$ , 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 · 2018-07-29T08:40:13

Below

Cup A
$V o l u m e = \frac{1}{3} π r^{2} h$ $Volume = 1/3pir^2h$
$V = \frac{1}{3} π {(12)}^{2} (38)$ $V=1/3pi(12)^2(38)$
$V = 1824 π$ $V=1824pi$

Cup B
$V o l u m e = \frac{1}{3} π r^{2} h$ $Volume=1/3pir^2h$
$V = \frac{1}{3} π {(18)}^{2} (24)$ $V=1/3pi(18)^2(24)$
$V = 2592 π$ $V=2592pi$

Therefore, since the volume of Cup A is less than the volume of Cup B, then Cup A will overflow.

Cups A and B are cone shaped and have heights of 38cm38 cm and 24cm24 cm and openings with radii of 12cm12 cm and 18cm18 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?