Question

a well whose diameter is 14m and 25m deep find the volume of mud taken out of the well also find cost of plastering the well from inside at the rate of Rs3 per square meter​

Answer 1

Answer:

Radius of the well, r = 2 m.

Depth of the well, h = 14 m.

Volume of the earth taken out.

=πr2H=(227×2×2×14)m3=176m3=πr2H=(227×2×2×14)m3=176m3

Let the width of the embankment be x metres.

Internal radius of the embankment, R = (2+x) m.

Height of the embankment, H=−40cm=(40100)mH=-40cm=(40100)m.

Volume of the embankment

=πH(R2−r2)={40100[(2+x)2−221}m3=πH(R2-r2)={40100[(2+x)2-221}m3

=[2π5(x2+4x)]m3=[2π5(x2+4x)]m3.

Now, volume of the embankent = volume of hte earth dug out

? ltBRgt ⇒ 25×227×(x2+4x)=176⇒x2+4x=176×5×72×22=140⇒ 25×227×(x2+4x)=176⇒x2+4x=176×5×72×22=140

⇒ x(x+14)−10(x+14)=0⇒(x+14)(x−14)=0⇒ x(x+14)-10(x+14)=0⇒(x+14)(x-14)=0

⇒ x=10 [∵≠−14]<