Question

A reservoir in the form of the frustum of a right circular cone contains 44 × 10⁷ litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir. (Take: $(\pi=\frac{22}{7})$ )

Answer 1

Answer:

Depth (h) of the reservoir is  24 m and Lateral Surface area of the reservoir is 26,145.42 m².

Step-by-step explanation:

SOLUTION :  

GIVEN :

Let ‘h’ be the height of the reservoir which is in the form of frustum of cone.

Radius of the top of the reservoir, R = 100 m

Radius of the bottom of the reservoir, r=  50 m

Volume of the reservoir = 44 × 10^7 litres

= 44 × 10^7 × 10^-3 = 44 × 10⁴ m³

[1 litres = 10^-3 m³]

Volume of the reservoir (frustum of Cone) = π/3  (R² + r² + Rr) h

= ⅓ × π (100² + 50² + 100× 50)× h

= ⅓ π (10000 + 2500 + 5000)× h

= ⅓ × 22/7  × 17500 × h

= (⅓ × 22 × 2500 × h)  

(44 × 10⁴) m³ = (⅓ × 22 × 2500 × h)  

h =  (44 × 10⁴  × 3) / (22 × 2500 )  

h = 12 × 10⁴ / 5000  

h = 12 × 10⁴ / 5 × 10³

h =  12 × 10 / 5 = 120/5 = 24 m

Depth (h) of the reservoir = 24 m

Slant height of a reservoir , l = √(R - r)² + h²

l =√(100 - 50)² + 24²

l = √50² + 576

l = √2500 + 576

l = √3076

l = 55.46 m

Lateral Surface area of the reservoir = π(R + r)l

= π(100 + 50) × 55.46

= π × 150 × 55.46

= 22/7 × 150 × 55.46

= 183,018/7

= 26,145.42 m²

Lateral Surface area of the reservoir = 26,145.42 m²

Hence, Depth (h) of the reservoir is  24 m and Lateral Surface area of the reservoir is 26,145.42 m².

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Answer 2

Step-by-step explanation:

lateral surface area =26145.42