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

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.

Try it free!

Register in 2 easy steps and start learning in 30 seconds!

Copyrights © 2019 All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

10-C, Kalinga Colony, Bobbili Raja Salai

K.K.Nagar, Chennai. India. Pin - 600 078

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com