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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)72π hours
- b)1 hour
- c)3 hours
- d)36π hours
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
An inverted right circular cone has a radius of 9 cm. This cone is par...
Given,
Surface area of oil = 36 π = πr2
⇒ r = 6 cm
Now,
∆ABC ~ ∆AED
Surface area of oil = 36 π = πr2
⇒ r = 6 cm
Now,
∆ABC ~ ∆AED
h = 6 cm
∴ Volume of oil in the cone = (1/3)πr2h
= (1/3)π62 x 6
= 72π
⇒ Time taken = 72π/1
= 72π hours.
Most Upvoted Answer
An inverted right circular cone has a radius of 9 cm. This cone is par...
To find the height of the cone, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height.
Since the cone is partly filled with oil up to a level 3 cm from the top, the height of the oil is the total height of the cone minus 3 cm.
So, h = total height - 3 cm
To find the total height, we can use the formula for the surface area of a cone:
A = πr(r + √(r^2 + h^2))
where A is the surface area.
Since the surface area is given as 36 cm^2, we can substitute the values into the equation:
36 = π(9)(9 + √(9^2 + h^2))
Now we can solve for h:
36/π = 81 + √(81 + h^2)
36/π - 81 = √(81 + h^2)
(36/π - 81)^2 = 81 + h^2
h^2 = (36/π - 81)^2 - 81
h = √((36/π - 81)^2 - 81)
Using a calculator, we find that h ≈ 6.81 cm.
Therefore, the height of the cone is approximately 6.81 cm.
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height.
Since the cone is partly filled with oil up to a level 3 cm from the top, the height of the oil is the total height of the cone minus 3 cm.
So, h = total height - 3 cm
To find the total height, we can use the formula for the surface area of a cone:
A = πr(r + √(r^2 + h^2))
where A is the surface area.
Since the surface area is given as 36 cm^2, we can substitute the values into the equation:
36 = π(9)(9 + √(9^2 + h^2))
Now we can solve for h:
36/π = 81 + √(81 + h^2)
36/π - 81 = √(81 + h^2)
(36/π - 81)^2 = 81 + h^2
h^2 = (36/π - 81)^2 - 81
h = √((36/π - 81)^2 - 81)
Using a calculator, we find that h ≈ 6.81 cm.
Therefore, the height of the cone is approximately 6.81 cm.
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Community Answer
An inverted right circular cone has a radius of 9 cm. This cone is par...
Given,
Surface area of oil = 36 π = πr2
⇒ r = 6 cm
Now,
∆ABC ~ ∆AED
Surface area of oil = 36 π = πr2
⇒ r = 6 cm
Now,
∆ABC ~ ∆AED
h = 6 cm
∴ Volume of oil in the cone = (1/3)πr2h
= (1/3)π62 x 6
= 72π
⇒ Time taken = 72π/1
= 72π hours.
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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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT 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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UCAT 2025 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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT 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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UCAT 2025 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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution 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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of 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)72π hoursb)1 hourc)3 hoursd)36π hourse)None of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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