The area of a circle varies with the square of its radius. The area of a circle having radius 3 cm is ` C cm^(2)`. Find the area of the circle having redius 9 cm.

Explanation

Let the area of the circle be denoted by C and its redius be denoted by r.
` C propto r^(2) rArr C_(1)/C_(2) = r_(1)^(2)/r_(2)^(2)`.
Taking `r_(1)= 3 cm, r_(2) = 9 cm and C_(1) = C cm^(2)`,
` C_(2) = C_(1) (r_(2)^(2)/r_(1)^(2)) = C (9/3)^(2) = 9C cm^(2)`.