Exemplar Exercise 11.1 (Area Related to Circles)

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

If the sum of the circumferences of two circles with radii R₁ and R₂ is equal to the circumference of a circle of radius R, then

If the circumference of a circle and the perimeter of a square are equal, then

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be

The area of the circle that can be inscribed in a square of side 6 cm is

The area of the square that can be inscribed in a circle of radius 8 cm is

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36cm and 20 cm is

The diameter of a circle whose area is equal to the sum  of the areas of the two circles of radii 24 cm and 7 cm is