CAT Practice : Mensuration

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Combo of Mensuration and Rate of Speed.

Right Circular Cone

    Q.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 1cm3/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

 

  • Correct Answer
    Choice A. 216π hours

Detailed Solution

Given,

Surface area of oil = 36 π = πr2

=) r = 6 cm

Now,

∆ABC ~ ∆AED

=

=)

=) h = 6 cm

∴ Volume of oil in the cone = πr2h

= π62 x 6

= 216π

=) Time taken = = 216π hours

Choice (A) is therefore, the correct answer.

Correct Answer: 216π hours



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More questions from Mensuration

  1. Cone and Frustum
  2. Spheres
  3. Circles and Chords
Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.