In the adjoining figure, A B C D is a square of side 20 cm . Four circles of equal radii 7 cm are drawn on its four vertices. Find the area of the shaded region. (Use π = 3 . 14 )

We have, each side of square A B C D = 20 cm ∴ Area of square A B C D = 20 2 = 400 cm 2 Now radius of each quadrant of circle = 20 2 cm = 10 cm ∴ The sum of the area of the four quadrants at the four corners of the square = 4 × πr 2 4 = πr 2 = π 10 2 = 3 . 14 × 100 = 314 cm 2 Now area of shaded portion = Area of square, A B C D - The sum of the areas of four quadrants at the four corners of the square = 400 - 314 cm 2 = 86 cm 2

A sector of arc length 22 cm and central angle 60 ° is cut off from a circular metal disc. Find the perimeter of the remaining portion of the disc.

Given, length of the arc = 22 cm Central angle, θ = 60 ° Length of an arc = θ 360 ° × 2 π r , where θ is the central angle and r is the radius of the circle ∴ 60 ° 360 ° × 2 × 22 7 × r = 22 ⇒ 1 6 × 2 × 1 7 × r = 1 ⇒ r = 6 × 7 2 ⇒ r = 21 Radius of the circle = 21 cm Circumference of a circle = 2 π r Circumference of the circle = 2 × 22 7 × 21 cm = 132 cm Perimeter of the remaining portion of the disc = Circumference of the circle - Length of the arc = 132 - 22 cm = 120 cm Hence, the required perimeter is 120 cm .

A rectangle of dimensions 16 cm × 12 cm is inscribed in a circle. Find the area enclosed between the circle and the rectangle.

Area of rectangle = 16 × 12 = 192 cm 2 In triangle B D C , By using Pythagoras theorem, B D 2 = B C 2 + C D 2 B D 2 = 16 2 + 14 2 B D 2 = 256 + 144 = 400 B D = 20 Diameter of circle = B D = 20 cm Radius of circle = Diameter 2 = 20 2 = 10 cm Area of circle = π × 10 2 = 3 . 14 × 100 = 314 cm 2 The area enclosed between the circle and the rectangle = Area of circle - Area of rectangle = 314 - 192 = 122 cm 2

A wire bent in the form of a square encloses an area of 1936 cm 2 . If the same wire is bent into a circle, find the area enclosed by it.

Given, a wire bent in the form of a square encloses an area of 1936 cm 2 . Area of a square = a 2 , where a is the length of the side of the square. ∴ a 2 = 1936 ⇒ a = 1936 ⇒ a = 44 Perimeter of a square = 4 × side Perimeter of the square = 4 × 44 cm = 176 cm Give, the same wire is bent into a circle. Circumference of the circle = Perimeter of the square Circumference of a circle = 2 π r , where r is the radius of the circle ∴ 2 × 22 7 × r = 176 ⇒ r = 176 × 7 44 ⇒ r = 28 Area of a circle = π r 2 = 22 7 × 28 cm × 28 cm = 2464 cm 2 Therefore, the area enclosed by the circle is 2464 cm 2 .

The length of a minute hand of a clock is 14 cm . Find the area swept by the minute hand in 10 minutes . [Use π = 22 7 ]

Given, length of a minute hand of a clock, r = 14 cm One complete rotation will sweep the circle fully with the radius of the circle being equal to the length of a minute hand in 60 minutes . Area of a circle = π r 2 , where r is the radius of the circle Area swept by the minute hand of the clock in 60 minutes = 22 7 × 14 cm 2 = 616 cm 2 Area swept by the minute hand of the clock in 1 minute = 616 60 cm 2 Area swept by the minute hand of the clock in 10 minutes = 616 60 × 10 cm 2 = 102 . 67 cm 2 Therefore, the required area is 102 . 67 cm 2 .

In a circle of radius 28 cm , an arc subtends an angle 90 ° at the centre. Find the perimeter of the sector.

Given, radius of circle = 28 cm , Arc A B subtends an angle 90 ° ⇒ ∠ A O B = 90 ° We know that, Perimeter of the sector A O B = Length of arcs O A + A B + O B Length of an arc = θ 360 ° × 2 πr , where θ is angle subtended at a centre and 2 πr is circumference of a circle. Length of an arc = 90 360 × 2 × 22 7 × 28 = 44 cm Perimeter of the sector A O B = 28 + 44 + 28 = 100 cm Hence, the perimeter of the sector A O B is 100 cm .

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Areas Related to Circles>Nagaland Board-2020>Q 8

MEDIUM

10th Nagaland Board

IMPORTANT

Earn 100

If the perimeter of a semicircle is $36 cm$ , then its radius is

50% studentsanswered this correctly

Important Questions on Areas Related to Circles

EASY

10th Nagaland Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Areas Related to Circles>Nagaland Board-2020>Q 9

Find the area of a quadrant of a circle whose circumference is

22 cm

in

{cm}^{2}

.

MEDIUM

10th Nagaland Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Areas Related to Circles>Nagaland Board-2020>Q 10

The wheels of a car are of diameter $80 c m$ each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of $66 k m$ per hour? $(use π = \frac{22}{7})$

MEDIUM

10th Nagaland Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Areas Related to Circles>Nagaland Board-2020>Q 11

The area of an equilateral triangle

A B C

is

17320.5 c m^{2} .

With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle as shown in the figure. Find the area of shaded region. (Use