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NCERT Solutions for class 10 Maths Chapter 12 Areas related to Circles

NCERT solutions for class 10 maths chapter 12 contain the correct answer and solutions to all those questions. Latest : Trouble with homework? Post your ncert solutions class 10th area related to circles view of Maths and Science with step-by-step solutions instantly. Ask Mr AL. Q1 The radii of 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. Circumference of 1st circle is given :. And the circumference of the 2nd circle is :. Thus the circumference of the new circle is. Hence the radius of the new circle is 28 cm. Q2 The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having an area equal to the sum of the areas of the two circles.

We know that the area of the circle is :. Thus area of a 1st circle :. And the area of a 2nd circle is :. According to the question area of the new circle is.

Hence the area wooden sailing dinghy for sale canada key the new circle is 10 cm. Q3 Fig. The diameter of the region representing the Gold score is 21 cm and each of the other bands is Find the area of each of the five scoring regions.

The radius of each scoring region can be found by adding The area of the golden region is :. Then the area of the blue region is :. And the area of the black region is :. Area of the white region is :. Q4 The wheels of a car are of diameter 80 cm. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?

Let the number of revolution of the wheel be n. The circumference of the wheel is given by Now, the speed of the car is given by Thus distance traveled in 10 minutes is:. According to the question, we get. Hence the number of revolutions made by the wheel is Q5 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 units C 4 units D 7 units. Let the radius of the circle be r. Then according to question, we can write Hence option A is correct. We know that the area of a sector having radius r and angle is given by Thus the area of the given sector is Q2 Find the area of a quadrant of a circle whose circumference is 22 cm. We are given the circumference of the circle.

Also, we know that the area of a sector is given by :. It is given that we need to find the area of a quadrant.

Hence the area becomes Q3 The length of the minute hand of a clock is 14 cm. Find the area swept by the minute ncert solutions class 10th area related to circles view in 5 minutes. The minute hand rotates o in one hour. We need to find rotation in 5 min. The area of the sector is given by :. Hence the area swept by minute hand in 5 minutes is.

Q4 A chord of a circle of radius 10 cm subtends a right angle at the center. Find the area of the corresponding : i minor segment. The angle in the wooden sailing dinghy for sale canada key sector is 90 o. Thus the area of the sector is given by Now the area of a triangle is Find the area of the corresponding : ii major sector.

The area of the major sector can be found directly by using the formula :. Thus the area is :. Find: i the length of the arc. The length of the arc is given by Hence the length of the arc is 22 cm. Find: ii area of the sector formed by the arc. We know that the area of the sector is given by Thus the area of the sector is cm 2. Find: iii area of the segment formed by the corresponding chord. For the area of the segment, we need to subtract the area of the triangle attached with the area of arc.

Thus consider the triangle It is given that the angle of arc is 60 oor we can say that all angles are 60 o since two sides are equal. Ncert solutions class 10th area related to circles view it is an equilateral triangle. Area of triangle is Hence the area of segment is Find the areas of the corresponding minor and major segments of the circle.

Use. The area of the sector is :. Now consider the triangle, the angle of the sector is 60 0. This implies it is an equilateral triangle. As two sides are equal so will have the same angle. This possible only when all angles are equal i. Thus, the area of the triangle is Hence area of the minor segment :.

And the area of the major segment is :. Find the area of the corresponding segment of the circle. For the area of the segment, we need the area of sector and area of the associated triangle. So, the area of the sector is :. Now, consider the triangle Draw a perpendicular from the center of wooden sailing dinghy for sale canada key circle on the base of the triangle let it be h.

Using geometry we can write. Thus the area of the triangle is :. Hence the area of segment is:. Q8 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 Fig. Find i the area of that part of the field in which the horse wooden sailing dinghy for sale canada key graze.

Find ii the increase in the grazing area if the rope were 10 m long instead of 5 m. When the length of the rope is 10 m, the area grazed will be Hence the change in the grazing area is given by :. Q9 A brooch is made with silver wire in the form of a circle with a diameter of 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig.

Find: i the total length of the silver wire required. The total wire required will be for 5 diameters and the circumference of the brooch.

RD Sharma Class 12 Solutions. They include every question in NCERT solutions, which are asked in previous year's board examinations. Chapter-5 Arithmetic Progressions. Chapter Surface Areas and Volume Chapter 7 - Coordinate Geometry. In the chapter 12, Areas Related to Circles, the discussion begins with a review of the concepts of the perimeter circumference and area of a circle. It has been noticed that one or two questions based on these theorems are always asked in the board exam.
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