# Thread: word problem involving integrals

1. ## word problem involving integrals

A bowl is in the shape of a hemisphere with a diameter 30 cm and water is poured into the bowl to a height of "h" cm. Find the volume of water in the bowl.

Help pleeeeeease!!!!! What do I do???

2. You can set up an integral using washers.

${\pi}\int_{-15}^{h-15}(225-y^{2})dy$

Evaluate the integral and it'll give the volume at any height h.

3. A few quick questions...

Where did you get your original function from??? aka the 225 and y^2

And why is the integral from -15 to h-15 ????

Thanks a bunch

4. The original function forms the equation for a circle, $x^{2}=r^{2}-x^{2}$ The square of 15 is 225.

It's -15 because if the diameter of the hemisphere is centered at the origin,the bottom would be at -15. Then, any height above that would be
h-15.

If you left h=15, you would get the full volume of the hemisphere.
$2250\pi$

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