Question

The width of a circular ring is equal to the radius of the inner circle of the ring. If the radii of the inner and outer circles are r and R then the area of the circular ring is

• A. $2\pi R^2$
• B. $2\pi r^2$
• C. $3\pi R^2$
• D. $3\pi r^2$

Answer 1

The correct option is D $3\pi r^2$

Since width of the circular ring is equal to $r$, then $R=r+r=2r$
Area of the region between two concentric circles with radius of outer circle R, and inner circle r $=\pi (R^2-r^2)$
So, Area of the ring $=\pi ({\left(2r\right)}^2-r^2)=4\pi r^2-\pi r^2=3\pi r^2$