Question

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Answer 1

(a) The perimeter of the shape is the sum of half a circumference and the diameter itself.

The circumference of a circle with radius
`r` is
`2\pi r`, and since
`d=2r` we can write the circumference as

`C=\pi d`

So, half a circumference is

`(C)/(2)=(\pi d)/(2)`

Ad we get the perimeter by addind the diameter:

`P=(\pi d)/(2)+d`

(b) Given the perimeter, we can solve for
`d`:

`51.42=(\pi d)/(2)+d=d\left((\pi)/(2)+1\right)`

So, we can divide both sides by the parenthesis and we have

`d=(51.42)/((\pi)/(2)+1)=(51.42)/(2.571)=20`