Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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

Ex 5.3, 16 Important

Ex 5.3, 17

Ex 5.3, 18 Important You are here

Ex 5.3, 19 Important

Ex 5.3, 20 Important

Chapter 5 Class 10 Arithmetic Progressions

Serial order wise

Last updated at May 29, 2023 by Teachoo

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 𝜋 = 22/7) Here we have to find total length, i.e., total circumference of all semicircles We know that Circumference of circle = 2πr So, Circumference of semicircle = 1/2 × 2πr = πr Circumference of 1st semi circle = π × 0.5 Circumference of 2nd semicircle = π × 1.0 Circumference of 3rd semicircle = π × 1.5 …. Circumference of 13th semicircle = π × 6.5 So, the series is π × 0.5, π × 1.0, π × 1.5, ……………., π × 6.5 Taking 𝜋 common = 𝜋 (0.5, 1.0, 1. 5, 2 …….6.5) = 𝝅 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 = 𝒏/𝟐 (𝒂+𝒍) Putting n = 13, a = 0.5, 𝑙 = 6.5 S = 13/2 (0.5+6.5) S = 13/2 × 7 S = 91/2 S = 45.5 Now, Length of spiral = 𝜋 × S = 𝝅 × 45.5 = 22/7 × 45.5 = 22 × 6.5 = 143 ∴ Length of spiral is 143 cm