Last updated at May 29, 2018 by Teachoo

Transcript

Ex 5.3 ,18 A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (take = 22/7) Here we have to find total length, i.e., total circumference of all semicircles We know that Circumference of circle = 2 r So, circumference of semicircle = 1/2 2 r = r Circumference of 1st semi circle = 0.5 Circumference of 2nd semicircle = 1.0 Circumference of 3rd semicircle = 1.5 . Circumference of 13th semicircle = 6.5 So, the series is 0.5, 1.0, 1.5, ., 6.5 Taking common = (0.5, 1.0, 1. 5, 2 .6.5) = S Where S is sum of series 0.5, 1.0, 1.5, 2 .6.5 For 0.5, 1.0, 1. 5, 2 .6.5 As difference is same, it is an AP S can be found by using formula S = /2 ( + ) Here n = 13, a = 0.5, = 6.5 Putting values in formula S = 13/2 (0.5+6.5) S = 13/2 7 S = 91/2 S = 45.5 Length of spiral = Sum of series = S = 45.5 = 22/7 45.5 = 22 6.5 = 143 Length of spiral is 143 cm

Class 10

Important Questions for Exam - Class 10

- Chapter 1 Class 10 Real Numbers
- Chapter 2 Class 10 Polynomials
- Chapter 3 Class 10 Pair of Linear Equations in Two Variables
- Chapter 4 Class 10 Quadratic Equations
- Chapter 5 Class 10 Arithmetic Progressions
- Chapter 6 Class 10 Triangles
- Chapter 7 Class 10 Coordinate Geometry
- Chapter 8 Class 10 Introduction to Trignometry
- Chapter 9 Class 10 Some Applications of Trignometry
- Chapter 10 Class 10 Circles
- Chapter 11 Class 10 Constructions
- Chapter 12 Class 10 Areas related to Circles
- Chapter 13 Class 10 Surface Areas and Volumes
- Chapter 14 Class 10 Statistics
- Chapter 15 Class 10 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.