Question

A small terrace at a football ground comprises $15$ steps each of which is $50$ m long and built of solid concrete.
Each step has a rise of $\frac{1}{4}$m and a tread of $\frac{1}{2}$m. Calculate the total volume of concrete required to build the terrace.

Answer 1

Dimensions in $1^{st}$ step $=$ $50\times 0.25\times 05$ m

Volume of first step $=6.25$ cubic m

Dimensions of second step$=$ $50\times 0.5\times 05$m

Volume of $2^{nd}$ step $=12.5$ cubic m

Dimensions of $3^{rd}$ step $=$ $50\times 0.75\times 05$ m

Volume of $3^{rd}$ step $=18.75$ cubic m

Now, we have $a=6.25,d=6.25$ and $n=15$

Sum of $15$ terms can be calculated as follows:

$S_{15}=\frac{15}{2}[2\times 6.25+14\times 6.25]$

$=\frac{15}{2}\times 100=750$

Volume of concrete $=750$ cubic m