Question

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?

Answer 1

8.7 cm(appx.)

Explanation:

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.)`