**NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles **are prepared by specialised experienced mathematic teacher. Maths are most important subject of board and with the help of this chapter-wise NCERT solution and little practices you can get very good marks in your respective board exam. It also help students to build a foundation of upcoming class 11th and 12th. Student can also check the **Important Question with solution for class 9 to class 12.**

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**Class 10 Maths Chapter 12 Areas Related to Circles Exercise 12** contain total 3 exercise that has 35 questions and it covered the topic ‘Perimeter and Area of a Circle’, ‘Areas of Combinations of Plane Figures’ and ‘Areas of Sector and Segment of a Circle’. Detailed answers of all the questions in Class 10 Maths Chapter 12 **Areas Related to Circles Exercise 12.1** provided in NCERT TextBook. **Check Previous chapter – NCERT Solutions for Class 10 Maths Chapter 11 Constructions**

### Important Formulas –

circumference = 2πr

area of the circle = πr ^{2}

Area of the sector of angle θ = (θ/360) × π r^{2}

Length of an arc of a sector of angle θ = (θ/360) × 2 π r where r is the radius of the circle

### Exercise 12.1

**Question 1.****The radii of the two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles.****Solution:**

**Question 2.****The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.****Solution:**

**Question 3.**

**Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.**

The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Solution:

**Question 4.****The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?****Solution:**

**Question 5.****Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is****(a) 2 units****(b) n units****(c) 4 units****(d) 7 units****Solution:**

### Exercise 12.2

**Question 1.****Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.****Solution:**

**Question 2.****Find the area of a quadrant of a circle whose circumference is 22 cm.****Solution:**

**Question 3.****The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.****Solution:**

**Question 4.****A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:****(i) minor segment****(ii) major segment (Use π = 3.14)****Solution:**

**Question 5.****In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:****(i) length of the arc.****(ii) area of the sector formed by the arc.****(iii) area of the segment formed by the corresponding chord.****Solution:**

**Question 6.****A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)****Solution:**

**Question 7.****A chord of a circle of the radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73).****Solution:**

**Question 8.****A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see figure). Find:**

(i) the area of that part of the field in which the horse can graze.

(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)

Solution:

**Question 9.****A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure.****Find:**

(i) the total length of the silver wire required.

(ii) the area of each sector of the brooch.

Solution:

**Question 10.**

**An umbrella has 8 ribs which are equally spaced (see Fig. 12.13). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.**

Solution:

**Question 11.****A car has two wipers which do not overlap.****Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.****Solution:**

**Question 12.****To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14)****Solution:**

**Question 13.****A round table cover has six equal designs as shown in the figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per cm². (Use √3= 1.7)**

Solution:

**Question 14.****Tick the correct answer in the following: Area of a sector of angle p (in degrees) of a circle with radius R is**

Solution:

### Exercise 12.3

Question 1.

**Find the area of the shaded region in Fig. 12.19, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.**

Solution:

Question 2.

**Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm, respectively and AOC = 40°.**

**Solution:**

Solution:

Question 3.

**Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.**

Solution:

**Question 4.****Find the area of the shaded region in the figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.**

Solution:

Question 5.

**From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.**

Solution:

**Question 6.****In a circular table cover of (he radius 32 cm, a design Is formed leaving an equilìtcral triangle ABC in the middle as shown in the figure. Find the area of the design (shaded region).**

Solution:

**Question 7.****In the figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.****Solution:**

Question 8.

**Fig. 12.26 depicts a racing track whose left and right ends are semicircular.**

**The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find:**

**(i) the distance around the track along its inner edge**

**(ii) the area of the track**

**.**

Solution:

**Question 9.****In the figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.**

Solution:

**Question 10.****The area of an equilateral triangle ABC is 17320.5 cm ^{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 (see figure). Find the area of the shaded region.**

**(Use π = 3.14 and √ 3 = 1.73205).**

Solution:

**Question 11.****On a square handkerchief, nine circular designs each of the radius 7 cm are made (see figure). Find the area of the remaining portion of the handkerchief.**

Solution:

Question 12.

**In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the**

**(i) quadrant OACB, **

**(ii) shaded region.**

Solution:

**Question 13.****In the figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)**

Solution:

Ex 12.3 Class 10 Maths Question 14.

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see figure). If ZAOB=30°, find the area of the shaded region.

Solution:

**Question 15.****In the figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.**

Solution:

**Question 16.****Calculate the area of the designed region in the figure common between the two quadrants of the circles of the radius 8 cm each.**

Solution: