Question

The ratio of circumference of $2$ circle is $3:4$ then what is the ratio of the corresponding areas.

Answer 1

Suppose there are two circles $A$ and $B$ having radius $r$ and $R$ respectively then

$r:R=3:4$

$r=3x,R=4x$

Area of $A=\pi r^2=\pi (3x{)}^2=9\pi x^2$

Area of $B=\pi r^2=\pi (4x{)}^2=16\pi x^2$

Ratio of areas of circle $AandB=\frac{9\pi x^2}{16\pi x^2}=\frac{9}{16}$

Hence, Ratio of areas of two circles is $9:16$.