Each step has a rise of 1 4 m and a tread of 1 2 m. (see Fig. 5.8). Calculate the total volume of concrete required to build the terrace.

Solution

As we can see from the given figure, the firststep is ½ m wide, 2^{nd} step is 1m wide and 3^{rd} stepis 3/2m wide. Thus we can understand that the width of step by ½ m each timewhen height is ¼ m. And also, given length of the steps is 50m all the time.So, the width of steps forms a series AP in such a way that;

½ , 1, 3/2, 2, ……..

Volume of steps = Volume of Cuboid

= Length × Breadth Height

Now,

Volume of concrete required to build the firststep = ¼ ×1/2 ×50 = 25/4

Volume of concrete required to build thesecond step =¼ ×1/×50 = 25/2

Volume of concrete required to build thesecond step = ¼ ×3/2 ×50 = 75/2

Now, we can see the volumes of concreterequired to build the steps, are in AP series;