How many cubic metres of earth must be dug out to sink a well `14 m` deep and having a radius of `4 m.` If the earth taken out is spread over a plot of dimension `(25 m xx 16 m)`. What is the height of the platform so formed?

Explanation

Clearly, we have `r = 4 m and h = 14m`
Volume of the earth dug out of the well
`= (pi r^(2)h) " cubic units " = ((22)/(7) xx 4 xx 4 xx 4 ) m^(3) = 704 m^(3)`
Area of the given plot `= (25 xx 16) m^(2) = 400 m^(2)`
Volume of the plantform formed = volume of the earth dug out
`= 704 m^(3)`
Height of the plantform `= (("volume in " m^(3))/("area in " m^(2)))`
`= ((704)/(400))m = (176)/(100)m = 1.76m`
Hence, the height of the platform so formed `= 1.76 m.`