The volume of concrete required to build the terrace, if
I. the terrace consists of 20 steps each 100 units long.
II. each step has a rise of 12m and a breadth of 12m.
Both statements are required to answer
Given, length of each step is 100 m and width is 12m.
Also, height of 1st step =12m
Height of 2nd step 12+12=2×12m
Height of 3rd 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
∴ Both statements are required.