Question

A small terrace at a football ground comprises of 15 steps each of which 50 m long and built of solid concrete.
$each \: step \: has \: a \: rise \: of \: \frac{1}{4} m \: and \: a \: tread \: of \: \frac{1}{2} m$
Calculate the total volume of concrete required to build the terrace ...

Quality answer Required !!!☺️


Don't spam

Try your best ✌️

Answer 1

$here \: is \: u \: \: r \: answer$

clearly shown in figure ,

$volume \: of \: the \: concrete \: required \: to \: build \: the \: 1st \: step \: 2nd \: step \: 3rd \: step \: as \: \frac{1}{4} \times \frac{1}{2} \times 50$

$2 \times \frac{1}{4} \times \frac{1}{2} \times 50 \: (3 \times \frac{1}{4} ) \: \times \frac{1}{2} \times 50$

50 / 8 , 2 * 50 / 8 , 3 * 50 / 8 ,..

now , total volume of concrete.

V =

$\frac{50}{8} + 2 \times \frac{50}{3} \times \frac{50}{8} + ..$

=

50 / 8 [ 1 + 2 + 3 + ...]

it's is an bracket forms an Ap with first term (a) = 1 , common difference (d)

=> 2 - 1 = 1

n of terms ( n) = 15

V =

$\frac{50}{8} \times \frac{15}{2} 2 \times 1 + (15 - 1) \: \times 1$


$sn \:$
= [ n / 2 { 2a + ( n - 1 ) d } ]



$\frac{50}{8} \times \frac{15}{2} \times (2 + 14) = \frac{25}{15} \div 8 \times 16 = 750 \: {m}^{3}$


total volume of concrete required to build the terrace is 750 m^3

be brainly.

Answer 2

Hey there !

Solution:

We know that the given step is in the form of a cuboid. So the Volume of step is same as that of Volume of a cuboid.

Measures of the Step:

Length = 50 m

Breadth = 1/2 m which is 0.5 m

Height = 1/4 m which is 0.25 m

So, the volume for the first step is:

=> 50 × 0.5 × 0.25 = 6.25 m³

For volume of second step, there is an increase in the width while the height has the same increase.

So, let us see the increase in width.

=> First Step = 1/2 m, Second Step = 1 m, Third Step = 3/2 m.... Fifteen steps.

So Let us calculate Volume of Second Step :

Volume = 50 × 0.25 × 1 = 12.5 m³

Volume of third step:

Volume = 50 × 0.25 × 1.5 = 18.75 m³

Now if we notice, the volumes are forming an AP.

=> 6.25 m³, 12.5 m³, 18.75 m³, ...

Here the common difference is 6.25 m³ and the first term is 6.25 m³.

Sum of volumes upto Fifteen steps is the required answer.

$\text{ Sum of n terms } = \dfrac{ n}{2} [ 2a + ( n - 1 ) d ]$

Here n is 15. Substituting the other values we get,

$\implies S_{15} = \dfrac{15}{2} [ \: 2 ( 6.25 ) + ( 15 - 1 ) \: 6.25 ] \\ \\ \implies S_{15} = 7.5\: [ 12.5 + ( 14 ) 6.25 ] \\ \\ \implies S_{15} = 7.5 \; [ 12.5 + 87.5 ] \\ \\ \implies S_{15} = 7.5 \: [ 100 ] \\ \\ \implies S_{15} = 750$

Hence the volume of Concrete required for 15 steps is 750 m³.

Hope my answer helped !