# CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

###### CAT Questions | CAT Mensuration Questions | Right Circular Cone
CAT Questions

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. 216π hours
2. 1 hour
3. 3 hours
4. 36π hours

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##### 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 = πr2h = π62 x 6 = 216π => Time taken = $\frac{216π}{1}\\$ = 216π hours. The question is " How long will it take the cone to be completely empty? " ##### Hence, the answer is 216π hours. Choice A is the correct answer. ###### 2IIM's Online CAT Coaching4000 off on CAT Online Course for CAT 2020. Vaild till Dec 16th Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Dec 14th, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ## CAT Preparation Online | CAT Geometry - Mensuration Videos On YouTube #### Other useful sources for Geometry Questions | Mensuration Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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