Rajesh has been given the task of designing a conical bottom tank for his client. Height of conical part is equal to its radius. Length of cylindrical part is the 3 times of its radius. Tank is closed from top. The cross section of conical tank is given below.
Answers
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Answer:
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Explanation:
Given:
Rajesh has been given the task of designing a conical bottom tank for his client.
Height of the conical part is equal to its radius.
Length of cylindrical part is the 3 times its radius.
The tank is closed from top.
To find:
If the radius of the cylindrical part is taken as 3 meters, what is the volume of above conical tank?
What is the area of metal sheet used to make this conical tank?
What is the ratio of the volume of the cylindrical part to the volume of the conical part?
The cost of the metal sheet is Rs 2000 per square meter and the fabrication cost is 1000 per square meter. What is the total cost of the tank?
Oil is to be filled in the tank. The density of oil is 1050 kg per cubic meter. What is the weight of oil filled in the tank?
Solution:
Finding the volume of the above conical tank:
Radius of the cylindrical part = Radius of the conical part = r = 3 m
Height of the cylindrical part = 3r = 3 × 3 = 9 m
Height of the conical part = r = 3 m
∴ The volume of the conical bottomed tank,
= Volume of cylinder + Volume of cone
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Finding the area of metal sheet used to make this conical tank:
Radius, r = 3 m
∴ Slant height, l =
∴ The area of the metal sheet used to make this conical tank is,
= [CSA of the cylindrical part] + [Area of the top of the cylindrical part] + [CSA of the conical part]
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=
=
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Finding the ratio of the volume of the cylindrical part to the volume of the conical part:
∴ The ratio of the volume of the cylindrical part to the volume of the conical part,
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Finding the total cost of the tank:
The cost of the metal sheet is = Rs 2000 per square meter
The fabrication cost is = Rs. 1000 per square meter
∴ The total cost of the tank per meter square is = Rs. 2000 + Rs. 1000 = Rs. 3000
∴ The total cost of the conical bottom tank is,
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Finding the weight of oil filled in the tank:
The density of the oil = 1050 kg per cubic meter
∴ The weight of the oil to be filled in the conical tank is,
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we know 1 kg = 0.001 tonne
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