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A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3 of ethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and the same for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost of accessories, piping and instruments can be taken as 10% of the cost of the wall. 10% of the volume of the tank needs to be kept free as vapour space above the liquid storage. What is the optimum diameter (in m) for the tank?
- a)3.5
- b)3.9
- c)7.5
- d)7.8
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A vertical cylindrical tank with a flat roof and bottom is to be const...
10% of tank volume to be kept free as vapour space
90% of tank volume to be used for liquid storage
90% of tank volume to be used for liquid storageh →height of tank
r→radius of tank
r→radius of tank
Most Upvoted Answer
A vertical cylindrical tank with a flat roof and bottom is to be const...
To find the optimum diameter for the tank, we need to consider the cost of materials and fabrication for the tank wall, roof, and bottom, as well as the cost of accessories, piping, and instruments.
1. Calculate the volume of the tank:
Given that 10% of the volume needs to be kept free as vapor space, the actual volume of liquid storage will be 90% of the total volume.
Let V be the total volume of the tank, then the volume of liquid storage is 0.9V.
Given that the volume of liquid storage is 150 m^3, we have:
0.9V = 150
V = 150 / 0.9
V = 166.67 m^3
2. Calculate the surface area of the tank:
The surface area of the tank is the sum of the areas of the wall, roof, and bottom.
Given that the tank is cylindrical, the surface area of the wall is given by:
A_wall = 2πrh
Given that the roof and bottom are flat, their surface areas are given by:
A_roof = πr^2
A_bottom = πr^2
3. Calculate the cost of the tank:
The cost of the tank is the sum of the costs of the wall, roof, and bottom, as well as the cost of accessories, piping, and instruments.
Given that the cost of the wall is Rs 6000 per m^2, the cost of the roof is Rs 2000 per m^2, and the cost of the bottom is Rs 4000 per m^2, we have:
Cost_wall = A_wall * 6000
Cost_roof = A_roof * 2000
Cost_bottom = A_bottom * 4000
Cost_accessories = 0.1 * (Cost_wall + Cost_roof + Cost_bottom)
Total_cost = Cost_wall + Cost_roof + Cost_bottom + Cost_accessories
4. Optimize the diameter:
To minimize the cost, we need to find the diameter that minimizes the total cost.
Since the volume of the tank is fixed, we can express the height h in terms of the diameter d:
V = πr^2h
h = V / (πr^2) = 166.67 / (π(d/2)^2) = 166.67 / (πd^2/4) = 666.67 / (πd^2)
Substitute this expression for h into the equation for the surface area of the wall and simplify:
A_wall = 2πrh = 2π(666.67 / (πd^2)) = 1333.33 / d
5. Substitute the expression for the surface area of the wall into the equation for the cost of the tank and simplify:
Total_cost = (1333.33 / d) * 6000 + πd^2 * 2000 + πd^2 * 4000 + 0.1 * ((1333.33 / d) * 6000 + πd^2 * 2000 + πd^2 * 4000)
Total_cost = (3999.99 / d) * 6000 + 3 * πd^2 * 2000 + 3 * πd^2 * 4000 + 0.1 * ((3999
1. Calculate the volume of the tank:
Given that 10% of the volume needs to be kept free as vapor space, the actual volume of liquid storage will be 90% of the total volume.
Let V be the total volume of the tank, then the volume of liquid storage is 0.9V.
Given that the volume of liquid storage is 150 m^3, we have:
0.9V = 150
V = 150 / 0.9
V = 166.67 m^3
2. Calculate the surface area of the tank:
The surface area of the tank is the sum of the areas of the wall, roof, and bottom.
Given that the tank is cylindrical, the surface area of the wall is given by:
A_wall = 2πrh
Given that the roof and bottom are flat, their surface areas are given by:
A_roof = πr^2
A_bottom = πr^2
3. Calculate the cost of the tank:
The cost of the tank is the sum of the costs of the wall, roof, and bottom, as well as the cost of accessories, piping, and instruments.
Given that the cost of the wall is Rs 6000 per m^2, the cost of the roof is Rs 2000 per m^2, and the cost of the bottom is Rs 4000 per m^2, we have:
Cost_wall = A_wall * 6000
Cost_roof = A_roof * 2000
Cost_bottom = A_bottom * 4000
Cost_accessories = 0.1 * (Cost_wall + Cost_roof + Cost_bottom)
Total_cost = Cost_wall + Cost_roof + Cost_bottom + Cost_accessories
4. Optimize the diameter:
To minimize the cost, we need to find the diameter that minimizes the total cost.
Since the volume of the tank is fixed, we can express the height h in terms of the diameter d:
V = πr^2h
h = V / (πr^2) = 166.67 / (π(d/2)^2) = 166.67 / (πd^2/4) = 666.67 / (πd^2)
Substitute this expression for h into the equation for the surface area of the wall and simplify:
A_wall = 2πrh = 2π(666.67 / (πd^2)) = 1333.33 / d
5. Substitute the expression for the surface area of the wall into the equation for the cost of the tank and simplify:
Total_cost = (1333.33 / d) * 6000 + πd^2 * 2000 + πd^2 * 4000 + 0.1 * ((1333.33 / d) * 6000 + πd^2 * 2000 + πd^2 * 4000)
Total_cost = (3999.99 / d) * 6000 + 3 * πd^2 * 2000 + 3 * πd^2 * 4000 + 0.1 * ((3999
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A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer?
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A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer?.
A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer?.
Solutions for A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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ample number of questions to practice A vertical cylindrical tank with a flat roof and bottom is to be constructed for storing 150m3ofethylene glycol. The cost of material and fabrication for the tank wall is Rs 6000 per m2 and thesame for the roof and the tank bottom are Rs 2000 and Rs 4000 per m2 respectively. The cost ofaccessories, piping and instruments can be taken as 10% ofthe cost of the wall. 10% of thevolume of the tank needs to be kept free as vapour space above the liquid storage.What is the optimum diameter (in m) for the tank?a)3.5b)3.9c)7.5d)7.8Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
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