10th CBSE math solution for exercise 5.3 part 10

This page 10th CBSE math solution for exercise 5.3 part 10 is going to provide you solution for every problems that you find in the exercise no 5.3 part 10

10th CBSE math solution for exercise 5.3 part 10

(17) In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in each they are studying ,e.g, a section  of class I will plant 1 tree, a section of class II will plant 2 trees and so on till class XII. There are three sections of each class. How many trees will be planted by the students?

Solution:

It can be observed that the number of trees planted by the student is in an AP

1,2,3,4,5,6,...............12

To find total number of trees planted we have to find the sum of 12 terms

 Sn= (n/2) [ 2 a + (n - 1) d]

S₁₂  = (12/2) [ 2 (1) + (12 - 1) (1)]

      = 6 [ 2 + 11 (1)]

      = 6(13)

      = 78

Total number of trees planted = 78


(18) A spiral is made up of successive semicircles,with centres alternately at A and B starting with center 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 spiral made up of thirteen consecutive semicircles. (∏ = 22/7)

Solution:

Semi perimeter of a circle = ∏r

radius of first semicircle = 0.5 cm

semi perimeter of first circle = ∏ (1/2) = ∏/2

radius of second semicircle = 1 cm

semi perimeter of second circle = ∏ (1) =

radius of third semicircle = 1.5 cm

semi perimeter of third circle = ∏ (3/2) = 3∏/2

(∏/2) + ∏ + (3∏/2) + ...........................


Sn= (n/2) [ 2 a + (n - 1) d]

   S₃ = (13/2) [2(∏/2)) + (13-1) ((∏/2))]

      = (13/2) [ ∏ + 6 ∏]

      = (13/2) [7∏]

      = 91∏/2

     = (91/2) x (22/7)

     = 143

Therefore the length of spiral of thirteen consecutive semicircles will be 143 cm.


In the page 10th CBSE math solution for exercise 5.3 part 10 next we are going to see the solution of next problem.

(16) A sum of Rs 700 is to be used to seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than the preceding prize, find the value of each prizes.

Solution:

x + (x - 20) + (x - 40) + ............... = 700

S n = 700

a = x     d = x - 20 - x     n = 7

               = -20 

 Sn= (n/2) [ 2 a + (n - 1) d]

   S = (7/2) [2(x) + (7-1) (-20)]

   700  = (7/2) [2x + 6(-20)]

    700 = (7/2) [2x - 120]

     (700 x 2)/7 =  2 x - 120

        200 = 2x - 120

           2x = 200 + 120

              2 x =  320

                x = 320/2 = 160    

The first prize amount Rs 160

 Second prize = Rs 140

 Third prize = Rs 120

 Fourth prize = Rs 100

 Fifth prize = Rs 80

 sixth prize = Rs 60

 Seventh prize = Rs 40




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