Question

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 m and a tread of m (See figure) calculate the total volume of concrete required to build the terrace.

Answer 1

From the figure, it can be observed that

1^st step is m wide,

2^nd step is 1 m wide,

3^rd step is m wide.

Therefore, the width of each step is increasing by m each time whereas their height m and length 50 m remains the same.

Therefore, the widths of these steps are

Volume of concrete in 1^st step

Volume of concrete in 2^nd step

Volume of concrete in 3^rd step

It can be observed that the volumes of concrete in these steps are in an A.P.

Volume of concrete required to build the terrace is 750 m³.