CAT 2020 Slot 1 QA Question 1: On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the

Question

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the

Accepted Answer

Let the radius of the circle be $r$ inches. Since the circle touches two opposite sides of the rectangle, one side of the rectangle is $2r$. Let the other side be $l$.

Painted area = $\pi r^2$
Unpainted area = $\dfrac{2}{3} \pi r^2$
Total area = $\pi r^2 + \dfrac{2}{3}\pi r^2 = \dfrac{5}{3}\pi r^2

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is