Question

A small terrace at a football ground comprises 15 steps each of which is 50m long amd built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m. Calculate the amount of concrete required to build the terrace.​

Answer 1

Answer:

Step-by-step explanation:

volume of each step = lbh

=> 50 * 1/2 * 1/4

=> 6.25m³

amount of concrete required to build 15 steps = 6.25*15 = 93.75 m³

Hope it helps! :)

Answer 2

$\mapsto \large\boxed{\red{\sf{Question:-}}}$

_______________

A small terrace at a football ground comprises 15 steps each of which is 50m long amd built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m. Calculate the amount of concrete required to build the terrace.

⠀⠀⠀⠀⠀⠀

$\mapsto \large\boxed{\green{\sf Concept:-}}$

_______________

•Here, the concept of Sum of n terms of Arithematic progression and volume of solid cuboid has been clarified.

⠀⠀⠀⠀⠀⠀

$\mapsto \large \boxed{ \sf\orange{Solution:-}}$

_______________

•Volume of concrete required to build the first step

$\implies \sf \dfrac{1}{4} \times \dfrac{1}{2} \times 50 {m}^{3}$

$\implies \sf \dfrac{25}{4} {m}^{3} .$

•Volume of concrete required to build the second step

$\implies \sf \bigg( \dfrac{1}{4} + \dfrac{1}{4} \bigg) \times \dfrac{1}{2} \times{ 50 m}^{3}$

$\implies \sf \dfrac{25}{2} {m}^{3}$

•Volume of concrete required to build third step

$\implies \sf \bigg( \dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4} \bigg) \times \dfrac{1}{2} \times 50 {m}^{3}$

$\implies \sf \dfrac{75}{4} {m}^{3}$

And so....on

⠀⠀⠀⠀⠀⠀

•Thus the volume (in m³) of concrete required to build the various step are

⠀⠀⠀⠀⠀⠀

$\longrightarrow \sf \dfrac{25}{4} \: , \: \dfrac{25}{2} \: , \: \dfrac{75}{4} .......$

Clearly list of numbers forms an A.P

$\sf Here, \: a= \dfrac{25}{4}$

$\: \: \: \: \: \: \sf \: d = \dfrac{25}{2} - \dfrac{25}{4} = \dfrac{25}{4}$

$\: \: \: \: \: \: \: \: \: \sf \: n = 15$

⠀⠀⠀⠀⠀⠀

∴Total volume of concrete required to build terrace

$\: \: \: \: \sf = S_n$

$\: \: \: \: \sf = S_{20}$

$\: \: \: \: \sf = \dfrac{15}{2} \{2a + (15 - 1)d \}$

$\: \: \: \: \sf =15(a + 7d)$

$\: \: \: \: \sf =(15) \bigg( \dfrac{25}{4} + 7 \times \dfrac{25}{4} \bigg)$

$\: \: \: \: \sf =(15)(50)$

$\: \: \: \: \sf = 750 {m}^{3}$

⠀⠀⠀⠀⠀⠀

Therefore ,total volume of concrete required to build terrace is 750m³

_________________

More to know:-

•The nth term of AP is a+(n-1)d.

•The sum of first nth terms of AP is n/2[2a+(n-1)d].

•Sum of the last nth term of AP is n/2(a+l).

•Three numbers in AP should be taken as :a-d,a,a+d.

•If a, b, c are in AP then, b=(a+c)/2 is called Arithematic mean of a and c.