# 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

Choice A. 216π hours

## Detailed Solution

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

Choice (A) is therefore, the correct answer.

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## More questions from Mensuration

Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.