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: π=22/7)
Answers
Depth (h) of the reservoir is 24 m and Lateral Surface area of the reservoir is 26,145.42 m².
Step-by-step explanation:
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 × 10⁷ litres
= 44 × 10⁷ × 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
h = 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
= 183018/7
= 26145.42 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.
Hope this answer will help you.....
similar questions :
A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many litres of milk it contains if it is full to the brim? If the milk is sold at Rs 40 per litre, find the amount received by the person.
https://brainly.in/question/8932564
A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs. 10 per 100 cm². (Use π = 3.14).
https://brainly.in/question/8925091
Answer:
Step-by-step explanation:
Volume of the reservoir = 44 × 10⁷ litres
= 44 × 10⁷ × 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
h = 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
= 183018/7
= 26145.42 m²