CBSE Class 10th Math 12 – Areas Related to Circles MCQs
Concentric circles are always equal in area.
Concentric circles have the same centre but different radii. Hence, the area of concentric circles is not equal.
Concentric circles are always equal in area.
The radius of the concentric circles differs from each other. Therefore the are as also differ.
A wire 44 cm long is in the form of a square. It is bent to form a circle. The area of the circle greater than that of the square is ____.
Given the length of the wire is 44 cm. Perimeter of the square = 4 × Side ⇒ 4 × Side = 44 ⇒ Side = 11 cm Area of the square = 11 × 11 = 121 cm2 The wire is bent into a circle. Circumference of the circle = πd ⇒ 44 =22/7 × d ⇒ d = 14 ⇒ r = 7 cm Area of the circle=π r2 = 22/7 × 49 = 154 cm2 Difference in area = 154 – 121 = 33 cm2 Hence, the area of the circle is 33 cm2 more than that of the square.
The distance covered by a wheel which has a diameter of 2 m in 700 revolutions is ____.
Given the diameter of the wheel is 2 m. Circumference of the wheel = πd = 22/7 × 2 = 44/7 Distance covered by the wheel = Circumference of the wheel × Number of revolutions = 44/7 × 700 = 4400 m = 4.4 km Hence, the distance covered by the wheel is 4.4 km.
The length of an arc of a sector of a circle with diameter d units and angle in degree measure θ is ____
The length of an arc of a sector of a circle with diameter d units and angle in degree measure θ is θ/360 πd
A wire in the form of an equilateral triangle of side 11 cm is bent to form a circle. The area of the circle is ____.
Given the side of equilateral triangle is 11 cm. The triangle-shaped wire is bent into a circle. Perimeter of the triangle = Circumference of the circle ⇒ 3 × Side = πd ⇒ 3 × 11 = 22/7 × d ⇒ d = (3 × 11 × 7)/22 ⇒ d = 10.5 cm ⇒ r = 10.5/2 cm Area of the circle = π r2 = 22/7 × 10.5/2 × 10.5/2 = 86.625 Hence, the area of circle is 86.625 cm2.
A circular park has a path of uniform width around it. If the difference between the outer and inner circumferences is 132 m, then the width of the path is ____.
Let the radius of the outer circle be R and radius of the inner circle be r. Circumference of outer circle=2πR Circumference of inner circle=2πr Given the difference between the outer and inner circumferences is 132 m. ⇒2πR − 2πr = 132 ⇒ R – r = 132/2π ⇒R − r = 66 × 7/22 ⇒ R − r = 21m Hence, the width of the path is 21 m.
A circular park has a path of uniform width around it. If the difference between the outer and inner circumferences is 132 m, then the width of the path is ____.
Let the radius of the outer circle be R and radius of the inner circle be r. Circumference of outer circle = 2πR Circumference of inner circle = 2πr Given the difference between the outer and inner circumferences is 132 m. ⇒ 2πR − 2πr = 132 ⇒ R – r = 132/2π ⇒ R – r = 66 × 7/22 ⇒ R − r = 21 m Hence, the width of the path is 21 m.
Area enclosed by two concentric circles is ____.
Let the outer radius be R cm and inner radius be r cm Area of outer circle= πR2 Area of Inner circle= πR2 Area between them= πR2− πR2 =π(R2−r2) Hence, the area of the enclosed two concentric circles is π(R2−r2).
Area of a sector of a circle with radius r units and angle in degrees measure θ is ____
Area of a sector of a circle with radius r units and angle in degrees measure θ is θ/360 × π r2
