Q. 54.3( 138 Votes )

# A small terrace at a football ground comprises of 15 steps each of which is 50 m long andbuilt of solid concrete.

Each step has a rise ofm and a tread ofm. (see Fig. 5.8). Calculate the total volumeof concrete required to build the terrace.

[Hint : Volume of concrete required to build the first step ]

Answer :

Dimensions of 1st step = 50 m x 0.25 m x 0.5 m

Volume of 1^{st} step = 6.25 m^{3}

Dimensions of 2^{nd} step = 50 m x 0.5 m x 0.5 m

Volume of 2^{nd}step = 12.5 m^{3}

Dimensions of 3^{rd}step = 50 m x 0.75 m x 0.5 m

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

Clearly, volumes of respective steps are in AP

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

Sum of 15 terms can be calculated as follows:

S_{15}

= 750

Hence, the volume of concrete will be 750m^{3}

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