The area of a circle is increased by 22 sq. cm when its radius is increased by 1 cm. What is the original radius of the circle? Use (22/7) as an approximation for (Pi)

Answer 1

Let say A₁=pi*r₁² and A₂=pi*r₂²

and also A₂=A₁+22 and r₂=r₁+1

Now we substitute A₁ and A₂ with their corresponding equations

A₂=A₁+22 --> pi*r₂² = pi*r₁² + 22 now substitute r₂ with r₁+1

pi*(r₁+1)² = pi*r₁² + 22 Expand

pi*(r₁²+2r₁+1)=pi*r₁² + 22

pi*r₁² + 2pi*r₁+ pi = pi*r₁² + 22

factor out pi and substitute pi=22/7 and solve for r₁