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 ]
Dimensions of 1st step = 50 m x 0.25 m x 0.5 m
Volume of 1st step = 6.25 m3
Dimensions of 2nd step = 50 m x 0.5 m x 0.5 m
Volume of 2ndstep = 12.5 m3
Dimensions of 3rdstep = 50 m x 0.75 m x 0.5 m
Volume of 3rdstep = 18.75 m3
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:
Hence, the volume of concrete will be 750m3
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The sum of n terms of an A.P. is 3n2+ 5n. Find the A.P. Hence, find its 16th term.KC Sinha - Mathematics