# CBSE Class 10th Math 12 – Areas Related to Circles MCQs

#### 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 cm^{2} 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 r^{2 } = 22/7 × 49 = 154 cm^{2} Difference in area = 154 – 121 = 33 cm^{2} Hence, the area of the circle is 33 cm^{2} 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 r^{2} = 22/7 × 10.5/2 × 10.5/2 = 86.625 Hence, the area of circle is 86.625 cm^{2}.

#### 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= πR^{2} Area of Inner circle= πR^{2} Area between them= πR^{2}− πR^{2} =π(R^{2}−r^{2}) Hence, the area of the enclosed two concentric circles is π(R^{2}−r^{2}).

#### 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 r^{2}