CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

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 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?

1. 72π hours
2. 1 hour
3. 3 hours
4. 36π hours

Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: Finding the Volume of oil in the cone will be the key.

Given,
Surface area of oil = 36 π = πr²
=> 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 = (1/3)πr²h
= (1/3)π6² x 6
= 72π
=> Time taken = \\frac{72π}{1}\\) = 72π hours.

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

Hence, the answer is 72π hours.

Choice A is the correct answer.