Solved Examples - Areas Related to Circles, CBSE, Class 10, Mathematics Class 10 Notes | EduRev

Class 10 : Solved Examples - Areas Related to Circles, CBSE, Class 10, Mathematics Class 10 Notes | EduRev

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Ex.1 Calculate the circumference and area of a circle of radius 5·6 cm.

Sol. We have :
Circumference of the circle  Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions
Area of the circle Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

 

Ex.2 The circumference of a circle is 123·2 cm. Calculate :
 (i) the radius of the circle in cm,
 (ii) the area of the circle, correct to nearest cm2.

Sol. (i) Let the radius of the circle be r cm.
Then, its circumference = (2πr) cm.
Class X, Mathematics, NCERT, CBSE, Q and A, Important, With SolutionsClass X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With SolutionsClass X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions
Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

 Ex.3 The area of a circle is 301·84 cm2. Calculate:

(i) the radius of the circle in cm.

(ii) the circumference of the circle, correct to nearest cm.

Sol. (i) Let the radius of the circle be r cm.
Then, its area = πr2 cm2 = 301.84
Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions
 Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions
= 61.6 cm.

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions Circumference of the circle, correct to nearest cm = 62 cm.

Ex.4 The perimeter of a semi-circular protractor is 32·4 cm. Calculate :

(i) the radius of the protractor in cm,

(ii) the area of the protractor in cm2.

Sol. (i) Let the radius of the protractor be r cm.

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions
Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Radius of the protractor = 6.3 cm.

(ii) Area of the protractor Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions Area of the protractor = 62·37 cm2.

 Ex.5 The area enclosed by the circumferences of two concentric circles is 346.5 cm2. If the circumference of the inner circle is 88 cm, calculate the radius of the outer circle.

Sol. Let the radius of inner circle be r cm.
Then, its circumference = (2πr) cm.

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With SolutionsClass X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Hence, the radius of the outer circle is 17·5 cm.

 Ex.6 Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Determine the radii of the circles.

Sol. Let the radii of the given circles be R cm and r cm respectively. As the circles touch externally, distance between their centres = (R + r) cm.

Class 10 Maths,CBSE Class 10,Maths,Class 10,Important Notes,Areas Related to Circles

Class 10 Maths,CBSE Class 10,Maths,Class 10,Important Notes,Areas Related to Circles  

 Ex.7 Two circles touch internally. The sum of their areas is 116π sq. cm and the distance between their centres is 6 cm. Find the radii of the given circles.

Sol. Let the radii of the given circles be R cm and r cm respectively. As the circles touch internally, distance between their centres = (R – r) cm.

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

 Ex.8 The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km/hr. Give your answer, correct to nearest km.

Sol. Radius of the wheel = 42 cm.

Circumference of the wheel =   Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions
Distance moved by the wheel in 1 revolution = 264 cm.
Distance moved by the wheel in 5 revolutions = (264 × 5) cm = 1320 cm.
Class X, Mathematics, NCERT, CBSE, Q and A, Important, With SolutionsDistance moved by the wheel in 1 second = 1320 cm.
Distance moved by the wheel in 1 hour = (1320 × 60 × 60) cm. 

Solved Examples - Areas Related to Circles, CBSE, Class 10, Mathematics Class 10 Notes | EduRev
Solved Examples - Areas Related to Circles, CBSE, Class 10, Mathematics Class 10 Notes | EduRev

Hence, the speed of the cart, correct to nearest km/hr is 48 km/hr.


Ex.9 The diameter of the driving wheel of a bus is 140 cm. How many revolutions must the wheel make in order to keep a speed of 66 km/hr?

Sol. Distance to be covered in 1 min.   Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions

Hence, the wheel must make 250 revolutions per minute.

Ex.10 A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 min. 28 seconds with a uniform speed of 1·1 m / sec, calculate the number of complete revolutions the wheel makes in raising the bucket.

Sol. Time taken by bucket to ascend = 1 min. 28 sec. = 88 sec. Speed = 1.1 m/sec.

Class X, Mathematics, NCERT, CBSE, Q and A, Important, With Solutions
Length of the rope = Distance covered by bucket to ascend
= (1·1 × 88) m = (1·1 × 88 × 100) cm = 9680 cm.

Solved Examples - Areas Related to Circles, CBSE, Class 10, Mathematics Class 10 Notes | EduRev

Circumference of the wheel Solved Examples - Areas Related to Circles, CBSE, Class 10, Mathematics Class 10 Notes | EduRev

Solved Examples - Areas Related to Circles, CBSE, Class 10, Mathematics Class 10 Notes | EduRev

Hence, the wheel makes 40 revolutions to raise the bucket.

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