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