Question

In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded region is 364π cm2. What is the value of x? Enter your answer in the box. x =

Answer 1

the picture in the attached figure

we know that
Area of circle=pi*r²
area of the shaded region=364*pi cm²
area of the shaded region=area of the outer circle -area of the inside circle

area of the outer circle=pi*[2x]²----> 4*x²*pi cm²
area of the inside circle=pi*6²------> 36*pi cm²
364*pi=4*x²*pi-36*pi------> 364=4*x²-36
4*x²=364+36-----> 4*x²=400
x²=400/4----> x²=100
x=10 cm

the answer is
x=10 cm