plz tell

Asked by  | 2nd Mar, 2010, 12:20: PM

Expert Answer:

1000 lit = 1 m3

44x107 lit = 44x104 m3

Let R and H be the initial radius and height of the cone before the frustrum is created,

and r and h be the radius and height of the cone that was cut off to make the frustrum.

tan α = R/H = r/h        ...... α - semivertical angle.

H = Rh/r = 100h/50 = 2h.

Volume of frustrum = Volume of Initial cone - Volume of cutoff cone

= (π/3)(R2H - r2h) = 44x104 m3

(π/3)(2R2 - r2)h = 44x104 m3

(π/3)(7)r2h = 44x104 m3           .........2R2 - r2 = 2(2r)2 - R2 = 8r2 - r2 = 7r2

(22/3)r2h = 44x104 m3

h = 3x44x104/(22x50x50) = 3x2x4 = 24 m

H = 2h = 48 m

Depth of water = 48 - 24 = 24 m

Lateral surface area = CSA of Initial cone - CSA of cutoff cone

= π(RS - rs)

= πr(2S - s)

= πr(2(R2 + H2) - (r2+h2))

= πr(4(r2 + h2) - (r2+h2))

= πr(3(r2 + h2)

= 22x50x3x(3076)/7

= 26122.46 m2.

Regards,

Team,

TopperLearning.

 

Answered by  | 2nd Mar, 2010, 01:37: PM

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