CBSE Class 10CBSE
Share
Notifications

View all notifications

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m (See figure) calculate the total volume of concrete required to build the terrace. - CBSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m (See figure) calculate the total volume of concrete required to build the terrace.

[Hint : Volume of concrete required to build the first step = 1/4 x 1/2 x 50m3]

Solution

From the figure, it can be observed that

1st step is 1/2 m wide,

2nd step is 1 m wide,

3rd step is 3/2 m wide.

Therefore, the width of each step is increasing by 1/2 m each time whereas their height 1/4 m and length 

50 m remains the same.

Therefore, the widths of these steps are

1/2,1, 3/2, 2,...

Volume of concrete in 1st step = `1/4 xx1/4 xx50 = 25/4`

Volume of concrete in 2nd step = `1/4 xx 1xx 50 = 25/2`

Volume of concrete in 3rd step = `1/4 xx 3/2 xx 50 = 75/4`

It can be observed that the volumes of concrete in these steps are in an A.P.

`25/4,25/2, 75/4,...`

a = 25/4

d = 25/2 - 25/4 = 25/4

and

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

`S_15 = 15/2[2(25/4)+(15-1)25/4]`

`=15/2[25/2+((14)25)/4]`

`= 15/2[25/2 + 175/2]`

=15/2(100) = 750

Volume of concrete required to build the terrace is 750 m3.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 5: Arithmetic Progressions
Ex. 5.40 | Q: 5 | Page no. 115
Solution A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m (See figure) calculate the total volume of concrete required to build the terrace. Concept: Sum of First n Terms of an AP.
S
View in app×