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Last updated at April 8, 2021 by Teachoo

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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, โฆโฆโฆ as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (take ๐ = 22/7) Here we have to find total length, i.e., total circumference of all semicircles We know that Circumference of circle = 2ฯr So, Circumference of semicircle = 1/2 ร 2ฯr = ฯr Circumference of 1st semi circle = ฯ ร 0.5 Circumference of 2nd semicircle = ฯ ร 1.0 Circumference of 3rd semicircle = ฯ ร 1.5 โฆ. Circumference of 13th semicircle = ฯ ร 6.5 So, the series is ฯ ร 0.5, ฯ ร 1.0, ฯ ร 1.5, โฆโฆโฆโฆโฆ., ฯ ร 6.5 Taking ๐ common = ๐ (0.5, 1.0, 1. 5, 2 โฆโฆ.6.5) = ๐ S Where S is sum of series 0.5, 1.0, 1.5, 2 โฆโฆ.6.5 For 0.5, 1.0, 1. 5, 2 โฆโฆ.6.5 As difference is same, it is an AP S can be found by using formula S = ๐/๐ (๐+๐) Putting n = 13, a = 0.5, ๐ = 6.5 S = 13/2 (0.5+6.5) S = 13/2 ร 7 S = 91/2 S = 45.5 Now, Length of spiral = ๐ ร S = ๐ ร 45.5 = 22/7 ร 45.5 = 22 ร 6.5 = 143 โด Length of spiral is 143 cm

Ex 5.3

Ex 5.3, 1 (i)

Ex 5.3, 1 (ii)

Ex 5.3, 1 (iii) Important

Ex 5.3, 1 (iv)

Ex 5.3, 2 (i)

Ex 5.3, 2 (ii)

Ex 5.3, 2 (iii) Important

Ex 5.3, 3 (i)

Ex 5.3, 3 (ii)

Ex 5.3, 3 (iii)

Ex 5.3, 3 (iv) Important

Ex 5.3, 3 (v)

Ex 5.3, 3 (vi) Important

Ex 5.3, 3 (vii)

Ex 5.3, 3 (viii) Important

Ex 5.3, 3 (ix)

Ex 5.3, 3 (x)

Ex 5.3, 4

Ex 5.3, 5

Ex 5.3, 6 Important

Ex 5.3, 7

Ex 5.3, 8

Ex 5.3, 9

Ex 5.3, 10 (i)

Ex 5.3, 10 (ii) Important

Ex 5.3, 11 Important

Ex 5.3, 12

Ex 5.3, 13

Ex 5.3, 14 Important

Ex 5.3, 15 Deleted for CBSE Board 2022 Exams

Ex 5.3, 16 Important Deleted for CBSE Board 2022 Exams

Ex 5.3, 17 Deleted for CBSE Board 2022 Exams

Ex 5.3, 18 Important Deleted for CBSE Board 2022 Exams You are here

Ex 5.3, 19 Important Deleted for CBSE Board 2022 Exams

Ex 5.3, 20 Important Deleted for CBSE Board 2022 Exams

Chapter 5 Class 10 Arithmetic Progressions (Term 2)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.