If the sum of the areas of two circles with radii \(R_1\) and \(R_2\) is equal to the area of a circle of radius \(R\), then
\(R_1 + R_2 = R\)
\(R_1^2 + R_2^2 = R^2\)
\(R_1 + R_2 < R\)
\(R_1^2 + R_2^2 < R^2\)
If the sum of the circumferences of two circles with radii \(R_1\) and \(R_2\) is equal to the circumference of a circle of radius \(R\), then
\(R_1 + R_2 = R\)
\(R_1 + R_2 > R\)
\(R_1 + R_2 < R\)
Nothing definite can be said about the relation among \(R_1, R_2\) and \(R\).
If the circumference of a circle and the perimeter of a square are equal, then
Area of the circle = Area of the square
Area of the circle > Area of the square
Area of the circle < Area of the square
Nothing definite can be said about the relation between the areas
Area of the largest triangle that can be inscribed in a semicircle of radius \(r\) is
\(r^2\) sq. units
\(\dfrac{1}{2}r^2\) sq. units
\(2r^2\) sq. units
\(\sqrt{2}\, r^2\) sq. units
If the perimeter of a circle is equal to that of a square, then the ratio of their areas (circle : square) is
\(22:7\)
\(14:11\)
\(7:22\)
\(11:14\)
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. The radius of the new park would be
10 m
15 m
20 m
24 m
The area of the circle that can be inscribed in a square of side 6 cm is
\(36\pi\,\text{cm}^2\)
\(18\pi\,\text{cm}^2\)
\(12\pi\,\text{cm}^2\)
\(9\pi\,\text{cm}^2\)
The area of the square that can be inscribed in a circle of radius 8 cm is
\(256\,\text{cm}^2\)
\(128\,\text{cm}^2\)
\(64\sqrt{2}\,\text{cm}^2\)
\(64\,\text{cm}^2\)
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
56 cm
42 cm
28 cm
16 cm
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
31 cm
25 cm
62 cm
50 cm