SOLUTION: show that the radius of a semicircle whose perimeter is numerically equal to its area is 2π+4/π

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Question 1117326: show that the radius of a semicircle whose perimeter is numerically equal to its area is
2π+4/π
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the circumference of a circle is equal to 2 * pi * r

the circumference of half a circle is equal to pi * r + 2 * r.

you are talking about half the circumference of the circle plus the length of the diagonal which is equal to 2 * r.

the area of the circle is equal to pi * r^2.

the area of half the circle is equal to pi * r^2 / 2

if the circumference of half the circle is equal to the area of half the circle, then:

pi * r + 2 * r = pi * r^2 / 2

multiply both sides of this equation by 2 to get:

2 * pi * r + 4 * r = pi * r^2

divide both sides of this equation by r to get:

2 * pi + 4 = pi * r

divide both sides of this equation by pi to get:

(2 * pi + 4) / pi = r

that's your solution.

you have r = (2 * pi + 4) / pi.

this is the same as what you are showing, except that you needed to put parentheses around 2pi + 4.

what you are showing as 2π+4/π should be (2π+4)/π