Question 1152782

The circumference of a circle  is:

{{{C=2r*pi}}}

 the area of the circle is:

{{{A=r^2*pi}}}

if the circumference of a circle is {{{2/3}}} the area of the circle, we have

{{{C=(2/3)A}}}.......substitute {{{C}}} and {{{A}}}

{{{2r*pi=(2/3)r^2*pi}}}...simplify

{{{2cross(r)*cross(pi)=(2/3)r^cross(2)*cross(pi)}}}

{{{2=(2/3)r}}}

{{{r=2/(2/3)}}}

{{{r=6/2}}}

{{{r=3}}}

check:

{{{C=2r*pi}}}=>{{{C=2*3*pi}}}=>{{{C=6*pi}}}

{{{A=r^2*pi}}}=>{{{A=3^2*pi}}}=>{{{A=9*pi}}}

{{{C=(2/3)A}}}=>{{{C=(2/3)9pi=(18/3)pi=6pi}}}