Q. 84.5( 14 Votes )

Two solid cones A and B are placed in a cylindrical tube as shown in the figure. The ratio of their capacities is 2 : 1. Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder.


Answer :

The diagram is:



Diameter of Cylinder = 6 cm


Radius of cylinder = r = 3 cm


[As radius = diameter/2]


As both cones have equal radius


Radius of cone A = radius of cone B = r = 3 cm


Let the height of cone A be h1 and Cone B be h2


Given,


Ratio of volume of cones is 2 : 1


i.e.



As volume of cone =


where r = base radius and h = height



h1 = 2h2


Now,


Total height of cylinder is 21 cm


h1 + h2 = 21


2h2 + h2 = 21


3h2 = 21


h2 = 7 cm


h1 = 2h2 = 2(7) = 14 cm






We know,


Volume of cylinder = πr2h ,


where r = radius and h = height


Volume of given cylinder = π(3)2(21)



Volume of remaining solid = (Volume of cylinder) – (volume of cone A) – (volume of cone B)


= 594 - 132 - 66 = 396 cm3


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Surface Area and VolumesSurface Area and VolumesSurface Area and Volumes43 mins
Quiz | Surface Area and VolumesQuiz | Surface Area and VolumesQuiz | Surface Area and Volumes42 mins
Surface Area and VolumeSurface Area and VolumeSurface Area and Volume49 mins
Areas Related to CircleAreas Related to CircleAreas Related to Circle36 mins
Quiz | Areas Related to CirclesQuiz | Areas Related to CirclesQuiz | Areas Related to Circles43 mins
Idioms and PhrasesIdioms and PhrasesIdioms and Phrases43 mins
Goprep Genius Quiz  | Analogy and ClassificationGoprep Genius Quiz  | Analogy and ClassificationGoprep Genius Quiz | Analogy and Classification48 mins
Acid - Types and NomenclatureAcid - Types and NomenclatureAcid - Types and Nomenclature52 mins
Agriculture and its ImportanceAgriculture and its ImportanceAgriculture and its Importance35 mins
Foundation | Permutation and CombinationFoundation | Permutation and CombinationFoundation | Permutation and Combination45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses