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Help needed calculating the area of a rectangle with 2 semi circles on either side

Attachment 31136

I start University in 3 months and im going over past papers for Mathematics. I have had a good deal of success with all questions bar one.

As i have finished up college i have no lecturers to ask how you would approach this and tbh its annoying me. I have spent 2 days and i feel i have hit a wall

Any help or tips would be appreciated

Re: Help needed calculating the area of a rectangle with 2 semi circles on either sid

Quote:

Originally Posted by

**dabeast** Attachment 31136 I start University in 3 months and im going over past papers for Mathematics. I have had a good deal of success with all questions bar one. As i have finished up college i have no lecturers to ask how you would approach this and tbh its annoying me. I have spent 2 days and i feel i have hit a wall Any help or tips would be appreciated

Specify the length of the rectangle

Re: Help needed calculating the area of a rectangle with 2 semi circles on either sid

You can use an integral to approximate it, but I don't know if that's the method you'd want to use.

The radius of the circle is $\displaystyle 2.0975 \pm 0.125$

The equation of the circle would be $\displaystyle x^2 + y^2 = (2.0975 \pm 0.125)^2$

And so the integral would be:

$\displaystyle \displaystyle \int _{-1.775 \mp 0.125} ^{1.775 \pm 0.125} \sqrt{ (2.0975 \pm 0.125)^2 - x^2 } \, \, dx$

This will give you the area of the left section. Just double it to get the area of the whole thing.