Question 332758
The number of centimeters in the perimeter of a semicircle is numerically the
same as the number of square centimeters in its area.
 What is the number of centimeters in the radius of the semicircle?
:
Let r = the radius
Half the circumference = {{{pi*r}}}
:
Circumference of a semi-circle = area of the semicircle
{{{(pi*r)+ 2r}}} = {{{.5*pi*r^2}}}
factor out r
{{{r(pi+2)}}} = {{{.5*pi*r^2}}}
Divide both sides by r
{{{pi+2}}} = {{{.5*pi*r}}}
Use 3.1416 for pi
3.1416 + 2 = .5*3.1416*r
5.1416 = 1.5708r
r = {{{5.1416/1.5708}}}
r = 3.273 cm is the radius
:
:
Check this:
 find the area of the semi circle
A = {{{.5*pi*3.273^2}}}
A = 16.827
:
Find the circum of the semi circle
C = {{{(pi*3.273)+2(2.373)}}}
C = 16.828, close enough