Question

Find the area of the circle, length of whose circumference is equal to the sum of the lengths of the circumferences with radii 15 cm and 13 cm.

Answer 1

In a circle

Circumference =Sum of circumferences of two circle of radii 15 cm and 13 cm

Now circumference of first smaller circle $=2\pi r$

$=2\times \frac{22}{7}\times 15=\frac{660}{7}cm$

Circumference of second smaller circle

$=2\times \frac{22}{7}\times 13=\frac{572}{7}cm$

$\therefore$ Circumference of bigger circle

$=\frac{660}{7}+\frac{572}{7}=\frac{1232}{7}cm$

Let R be its radius, then

$2\pi R=\frac{1232}{7}\Rightarrow \frac{2\times 22}{7}R=\frac{1232}{7}$

$\Rightarrow R=\frac{1232}{7}\times \frac{7}{44}=28cm$

$\therefore$ Area of the circle $=\pi R^2$

$=\frac{22}{7}\times 28\times 28c{m}^2=2464c{m}^2$