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. Calculate the total volume of concrete required to build the terrace.

Volume of concrete required to build the first step = 1/4 × 1/2 × 50 = 1/4 × 25 m³
Volume of concrete required to build the second step = 2/4 × 1/2 × 50 = 2/4 × 25 m³
Volume of concrete required to build the third step = 3/4 × 1/2 × 50 = 3/4 × 25 m³
Volume of steps are increasing in AP, whose first term a = 1/4 × 25 and the last term
a₁₅ = 15 /4 × 25. The common difference d = 2/4 × 25 – 1/4 × 25 = 1/4 × 25.
Therefore, the total volume of concrete required to build the terrace = S₁₅
= 15/2[(1/4 × 25) + (15 – 1)(1/4 × 25)]
= 15/2[25/2 + 175] = 15/2 ×200/2 = 750m³
Hence, the total 750m³ valume of concrete required to build the terrace.