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Question

A staircase consists of 20 steps. The length and breadth of each step is 100 m and 12 m respectively. The height of the lowermost step is 12 m and the height of the subsequent step increases by 12 m. Find the volume in m3 of the concrete required to make the staircase.



A

5250

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B

2520

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C

5225

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D

5520

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Solution

The correct option is A

5250


Given, length of each step is 100m and width is 12m.
Also, height of 1st step =12m
Height of IInd step 12+12=2×12m
Height of IIIrd step =32m
and so on.
Let V1, V2, V3, V20, denotes respectively the volume of the concrete required to build the 1st, 2nd, 3rd, . . ., 20th step.
Then,
V1=(100×12×12)m3V2=[100×12×(2×12)]m3V3=[100×12×(3×12)]m3
and so on.
Total volume
=V1+V2++V20=(100×12×12)+[100×12×(2×12)]+[100×12×(3×12)]++[(100×12×(20×12))]=100×12[12+22+32+42++202]=100×12×12[1+2++20]=25[202(2+19×1)]=25×10×21=5250 m3


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