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An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from a hole in the tip at a rate of 1cm2/hour. Currently the level of oil 3 cm from top and surface area is 36π cm2. How long will it take the cone to be completely empty?
- a)216π hours
- b)1 hour
- c)3 hours
- d)36π hours
Correct answer is option 'A'. Can you explain this answer?
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To find the volume of the cone, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
Given that the radius is 9 cm and the oil level is 3 cm from the top, we can find the height of the cone:
h = 9 - 3 = 6 cm
Substituting the values into the formula, we get:
V = (1/3)π(9^2)(6)
V = (1/3)π(81)(6)
V = (1/3)(486π)
V = 162π
Now, to find the rate at which the oil is dipping, we need to find the rate at which the volume is changing. This can be calculated using the formula:
dV/dt = A
Where dV/dt is the rate of change of volume with respect to time, and A is the surface area of the oil.
Given that the surface area is 36 cm^2, we can find the rate of change of volume:
dV/dt = 36 cm^2/hour
Therefore, the rate at which the oil is dipping is 36 cm^2/hour.
V = (1/3)πr^2h
Given that the radius is 9 cm and the oil level is 3 cm from the top, we can find the height of the cone:
h = 9 - 3 = 6 cm
Substituting the values into the formula, we get:
V = (1/3)π(9^2)(6)
V = (1/3)π(81)(6)
V = (1/3)(486π)
V = 162π
Now, to find the rate at which the oil is dipping, we need to find the rate at which the volume is changing. This can be calculated using the formula:
dV/dt = A
Where dV/dt is the rate of change of volume with respect to time, and A is the surface area of the oil.
Given that the surface area is 36 cm^2, we can find the rate of change of volume:
dV/dt = 36 cm^2/hour
Therefore, the rate at which the oil is dipping is 36 cm^2/hour.
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An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from a hole in the tip at a rate of 1cm2/hour. Currently the level of oil 3 cm from top and surface area is 36π cm2. How long will it take the cone to be completely empty?a)216π hoursb)1 hourc)3 hoursd)36π hoursCorrect answer is option 'A'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from a hole in the tip at a rate of 1cm2/hour. Currently the level of oil 3 cm from top and surface area is 36π cm2. How long will it take the cone to be completely empty?a)216π hoursb)1 hourc)3 hoursd)36π hoursCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An inverted right circular cone has a radius of 9 cm. This cone is partly filled with oil which is dipping from a hole in the tip at a rate of 1cm2/hour. Currently the level of oil 3 cm from top and surface area is 36π cm2. How long will it take the cone to be completely empty?a)216π hoursb)1 hourc)3 hoursd)36π hoursCorrect answer is option 'A'. Can you explain this answer?.
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