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.

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 Volumes43 mins
Quiz | Surface Area and Volumes42 mins
Surface Area and Volume49 mins
Areas Related to Circle36 mins
Quiz | Areas Related to Circles43 mins
Idioms and Phrases43 mins
Goprep Genius Quiz | Analogy and Classification48 mins
Acid - Types and Nomenclature52 mins
Agriculture and its Importance35 mins
Foundation | 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
view all courses