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.
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