This question is from CAT Mensuration in CAT Geometry. In this question, there ia an inverted right circular cone and filled with oil which is dipping at a cetrtain rate and we need to find the time taken to empty the cone with the given condtions. Mensuration Questions in the CAT exam can be solved with practical approach and thought process rather than just knowing theorems from CAT Geometry. Even if one is not completely prepared for CAT Geometry exam, he or she should be able to do well in Mensuration problems tested by the CAT Exam. Knowing Mensuration formulas is important. Make sure you master Mensuration questions for CAT exam. Its's a fabulous question with the Combo of Mensuration and Rate of Speed.

Question 8: 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 1cm^{2}/hour. Currently the level of oil 3 cm from top and surface area is 36π cm^{2}. How long will it take the cone to be completely empty?

- 216π hours
- 1 hour
- 3 hours
- 36π hours

216π hours

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Given,

Surface area of oil = 36 π = πr^{2}

=> r = 6 cm

Now,

∆ABC ~ ∆AED

=> \\frac{DE}{BC}\\) = \\frac{AE}{AC}\\)

=> \\frac{9}{6}\\) = \\frac{(3 + h)}{h}\\)

=> h = 6 cm

∴ Volume of oil in the cone = πr^{2}h

= π6^{2} x 6

= 216π

=> Time taken = \\frac{216π}{1}\\) = 216π hours.

The question is **" How long will it take the cone to be completely empty? "**

Choice A is the correct answer.

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