1.

It is required to make a plastering of sand and cement with 3*5 cm thick, surroundingfour cylindrical pillars, each of whose diameter is 17*5 cm. and height 3 m. If the ratio of sand and cement in the plaster material be 4:1 , then how many cubic, dcm of cement will be needed ?

Answer»

SOLUTION :Diameter `= 17.5 cm = 1.75 dcm`
`:.` Radius `= (1.75)/(2)` dcm `=0.875` dcm
Thickness of each pillar `= 3.5 cm = 0.35 dcm`
`:. ` Outer radius of the pillars after plastering will be `(0.875+0.35) dcm = 1.225` dcm
`:.` Volume of MATERIALS `= (22)/(7) {(1.225)^(2)-(0.875)^(2)}xx30` cubic.dcm [ `:'3m=30 dcm`]
`= (22)/(7) xx (1.225 + 0.875) (1.225-0.875)(1.225-0.875)xx30` cubic-dcm
`= (22)/(7) xx 2.1 xx 0.35 xx 30` cubic - dcm `= 69.3` cubic . dcm
`:. ` Volume of materials needed for 4 pillars `= 69.3xx4` cubic.dcm `= 277.2` cubic.dcm
`:.` Volume of materials needed for 4 pillars `= 69.3xx 4` cubic.dcm ` = 277.2` cubic.dcm
`:.` (a) 277.2 cubic.dcm plaster materials will be needed . (b) The RATIO of sand and cement is4:1
`:.` part of cement `= (1)/(4+1)=(1)/(5)`.
Hence the required cement `= 277.2xx( 1)/(5)` cubic.dcm` = 55.44` cubic . dcm .


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