Question

# A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Solution

## Inner diameter of well =14 m ∴ Inner radius =142=7m Depth (h)=12 m ∴ Volume of earth dig out =πr2h =227×(7)2×12m3 =227×7×7×12m3=1848m3 Width of the embankment of the well =7 m ∴ Outer radius (R)=7+7=14 m. Let height of the embankment =h ∴ Volume =πR2h=πr2h =πh(R2−r2)=227h(R2−r2) ∴227h(142−72)=1848 ⇒227(14+7)(14−7)=1848 ⇒227h×21×7=1848 ⇒462h=1848 ∴h=1848462=4 ∴ Height of embankment =4 m

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