# 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 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

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