Question

Please give the answer step by step. ​

Answer 1

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Dimensions of 1st step = 50 m x 0.25 m x 0.5 m

Volume of 1st step = 6.25 m3

Dimensions of 2nd step = 50 m x 0.5 m x 0.5 m

Volume of 2ndstep = 12.5 m3

Dimensions of 3rdstep = 50 m x 0.75 m x 0.5 m

Volume of 3rdstep = 18.75 m3

Clearly, volumes of respective steps are in AP

Now, we have a = 6.25, d = 6.25 and n = 15

Sum of 15 terms can be calculated as follows:

S15

= 750

Hence, the volume of concrete will be 750m3

Answer 2

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Sum of n terms of an AP

The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by

Sn = n /2 [ 2a + ( n - 1) d] or

Sn=n /2 [ a + l ]       (l = last term)-----------------------------------------------------------------------------------------------------

 volume of cuboid = l ×b×h 

[ solution & figure is in the attachment]

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Hence, the total volume of concrete required to build the terrace is 750

 

m³

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