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. Fig. Calculate the total volume of concrete required to build the terrace. [Hint : Volume of concrete required to build the first step = 1/4 × 1/2 ×50 m3.]
As we can see from the given figure, the first step is 1/2 m wide, 2nd step is 1m wide and 3rd step is 3/2m wide.
1/2, 1, 3/2, 2, ……..
Volume of steps = Volume of Cuboid
= Length × Breadth Height
Volume of concrete required to build the first step = 1/4 ×1/2 ×50 = 25/4
Volume of concrete required to build the second step = 1/4 ×1/×50 = 25/2
Volume of concrete required to build the second step = 1/4 ×3/2 ×50 = 75/2
25/4, 25/2, 75/2 …..
First term, a = 25/4
Common difference, d = 25/2 – 25/4 = 25/4
Sn = n/2[2a+(n-1)d]
= 15/2(2×(25/4 )+(15/2 -1)25/4)
we get,
Sn = 15/2 (100)
Sn= 750
Hence, the total volume of concrete required to build the terrace is 750 m3.