Question

a small pateform is made in a cricket ground.it has 15 stairs.length of each stairs is 50m and it is made of solid cconcrete. height and breadth of each stairs is 1/4m and 1/2m respectively. find the total volume in construction of a plateform.

Answer 1

Hi,
height of 1st step =1/4 m.
 height of second step=1/4+1/4 =2 × 1/4
height of 3rd step = 3 × 1/4 and so on.

V=volume
V1= (50×1/2×1/4),V2=)50×1/2×(2×1/4)) ,and so on
total volume of concrete = V1+V2+.........+V15
= (50×1/2×1/4)+(50×1/2×(2×1/4))+.............+(50×1/2×(15×1/4)) m³
=(50×1/2)(1/4+1/2+........+15/4)
=25(1/4+1/2+.......+15/4)
=25/4(1+2+.....+15)
=25/4×15/2(1+15)            ∴ use Sn = n/2(a+l)  
=25/4×15/2×16
=750 m³