The radii of two circles are 48 cm and 13 cm. Find the area of the circle which has its circumference equal to the difference of the circumferences of the given two circles.

Circumference of a circle = 2πr

For the first circle,

r₁ = 48 cm

Circumference₁ = 2 x π x 48 = 96π cm

For the second circle,

r₂ = 13 cm

Circumference₂ = 2 x π x 13 = 26π cm

Total circumference = Circumference₁ - Circumference₂

= 96π - 26π

= 70π cm

Let the radius of the new circle be R.

Circumference of the new circle = 2πR

70π = 2πR

70 = 2R

R = $\dfrac{70}{2}$

R = 35 cm

And, area of the new circle = πr²

$= \dfrac{22}{7} \times 35^2\\[1em] = \dfrac{22}{7} \times 1,225\\[1em] = \dfrac{26,950}{7}\\[1em] = 3,850 \text{ cm}^2$

Hence, the area of new circle is 3,850 cm².