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# perimeter watch

1. The circle (diameter 16cm) and the semicircle, including its diameter, have the same perimeter. Work out the radius, r, of the semicircle.
So far...
I worked out the perimeter of the circle being 16pie and I know that this would be the same as the perimeter of the semicircle.
2. (Original post by neharajput)
The circle (diameter 16cm) and the semicircle, including its diameter, have the same perimeter. Work out the radius, r, of the semicircle.
So far...
I worked out the perimeter of the circle being 16pie and I know that this would be the same as the perimeter of the semicircle.
1. Pi x 16 = 0.5 x 2 x Pi x r + 2r

2. Pi x 16 = 1 x Pi x r + 2r

3. Pi x 16 = r (Pi +2)

4. Pi x 16 / Pi +2 = r = 9.776cm

1. they equal each other. 0.5 because it is a semicircle. 2r for the diameter. 2 x Pi x r for the perimeter.
2. simplify.
3. factorise.
4. rearrange.

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