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.

= (1³ + 2³ + ......... + 30³) - (1³ + 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
- Special series
- Sequence
- Arithmetic progression
- Arithmetic series
- Geometric progression
- Geometric series

special series worksheet solution4.

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”