Last updated at Dec. 8, 2016 by Teachoo
Ex 13.3, 4 A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. Both well and embankment are in the from of cylinder. Let well be cylinder A and embankment be cylinder B. Since mud of well is distributed in embankment Volume of well = Volume of embankment Volume of well For cylinder A, Diameter = 3 m So, radius = r = 3/2 m = 1.5 m Height = 14 m Volume of cylinder A = 𝜋𝑟2ℎ = π×(1.5)2×(14) = π×2.25×14 = 31.5 𝜋 m3 So, Volume of well = Volume of cylinder A = 31.5 𝜋 m3 Volume of the embankment For cylinder B Cylinder B is a hollow cylinder with Inner Diameter = Diameter of well = 3 m Internal radius = r1 = 3/2 = 1.5 m External radius = r2 = internal radius + width = 1.5 + 4 = 5.5 m Volume of cylinder with internal radius = 𝜋𝑟12ℎ = 𝜋ℎ(1.5)2 Volume of cylinder with external radius = 𝜋𝑟22ℎ = 𝜋ℎ(5.5)2 Volume of cylinder B = Volume of cylinder with external radius – Volume of cylinder with internal radius = 𝜋ℎ(5.5)2−πh(1.5)2 = 𝜋ℎ((5.5)2−(1.5)2) = 𝜋ℎ(30.25−2.25) = 𝜋ℎ(28) = 28𝜋ℎ m3 So, Volume of embankment = 28𝜋ℎ m3 Now, Volume of well = Volume of embankment 31.5 π = 28 πh 28 𝜋h = 31.5 𝜋 h = 31.5/28 h = 1.125 Hence, the height of the embankment = 1.125 m.
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