Question 544932
I understand that in this problem you are trying to find the radius of a pie, knowing that a 2-radian slice has an area of 10 square meters.
That is quite a large pizza! Or is it apple pie?
A whole circle of radius {{{r}}} has an area equal to
{{{A=pi*r^2}}}
and, taken as an angle, measures, in radians, {{{2pi}}}
So the area of a 2-radian slice is
{{{(2/2pi)(pi*r^2)=2pi*r^2/(2pi)=cross(2pi)*r^2/(cross(2pi))=r^2}}}
So if {{{r^2=10m^2}}}, then, in meters, {{{r=sqrt(10)}}},
or approximately 3.16 meters.