Cups A and B are cone shaped and have heights of $35 cm$ and $21 cm$ and openings with radii of $14 cm$ and $9 cm$ , 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 · 2017-04-22T06:20:02

8.7 cm(appx.)

The volume of cup B = $1/3 pi r^2 h = 1/3xx pixx 9^2xx 21 cm^3$

The volume of cup A = $1/3 pi r^2 h = 1/3xxpixx14^2xx35 cm^3$

By seeing the above result it can say that cup A will not overflow.

Now , if B's contents poured in cup B, let it's height will be = x cm.

So, as per questions, $1/3xxpixx14^2xx x = 1/3xxpixx9^2xx21$

$rArr x = [1/3xxpixx9xx9xx21]/[1/3xxpixx14xx14]$

$rArr x = 8.7cm(appx.)$

Cups A and B are cone shaped and have heights of 35 cm35 cm and 21 cm21 cm and openings with radii of 14 cm14 cm and 9 cm9 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?