## Special Series Worksheet Solution4

In this page special series worksheet solution4 we are going to see solution  for each problems in the worksheet.

(11) Find the total area of 12 squares whose sides are 12 cm,13 cm,....... 23 cm respectively.

Solution:

To find total surface area of 12 squares we have to apply the formula for sum of squares of n natural numbers.

Sum of squares of n natural numbers = n(n+1)(2n+1)/6

Total surface area of 12 squares = 12² + 13² + ......... + 23²

We have to find sum of squares from 1 up to 23 and subtract the sum of squares of series from 1 up to 11 from that.

= (1² + 2² + ......... + 23²) - (1² + 2² + ......... + 11²)

= [23(23+1)(2x23+1)]/6 - [11(11+1)(2x11+1)]/6

= (23 x 24 x 47)/6 - (11 x 12 x 23)/6

= 4324 - 506

=  3818

(12) Find the total volume of 15 cubes whose edges are 16 cm,17cm,18 cm,....... 30 cm respectively.

Solution:

To find total volume of 15 cubes we have to apply the formula for sum of cubes of n natural numbers.

Sum of cubes of n natural numbers = [n(n+1)/2]²

Total volume of 15 cubes = 16³ + 17³ + 18³ +  ......... + 30²

We have to find sum of squares from 1 up to 30 and subtract the sum of squares of series from 1 up to 15 from that.

= ( + 2³ + ......... + 30³) - ( + 2³ + ......... + 15³)

= [30(30+1)/2]² - [15(15+1)/2]²

= [(30 x 31)/2]² - [(15 x 16)/2]²

= [(15 x 31)]² - [(15 x 8)]²

= [465]² - [120]²

= (465 + 120) (465 - 120)

=  585 x 345

=   201825

These are the contents in the page special series worksheet solution4.

special series worksheet solution4.

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