CBSE Class 10 Answered

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.