Question

If the radius of a circle is doubled then the ratio of the areas of the new circle and the old circle is

(A) 1 : 2 

(B) 1 : 4

(C) 4 : 1 

(D) 2 : 1

Answer 1

Correct Option (C) 4 : 1

Let the radius be r, then new radius = 2r

\(\text { Area }  =\pi r^{2}\)

\(\text { New Area }  =\pi(2 r)^{2}\)

\(=\frac{\text { Area of New Circle }}{\text { Area of old Circle }}\)

\( =\frac{{}{\not\pi}(2 r)^{2}}{\not\pi r^{2}}\)

\( =\frac{4 r^{2}}{r^{2}}\)

\( =\frac{4}{1}\)

= 4 : 1

Answer 2

If the radius of a circle is doubled then the ratio of the areas of the new circle and the old circle is (C) 4 : 1