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Question

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


A

376 cm3

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B

386 cm3

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C

396 cm3

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D

406 cm3

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Solution

The correct option is C

396 cm3


The diameter of the cylinder is 6 cm.
Thus, the radius of the cylinder is 3 cm.

The capacities of A and B are in the ratio 2:1

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

Let the heights of cone A and B be ha and hb respectively.

Assuming the thickness to be negligible, we can say that the volumes of cones A and B are in the ratio 2:1

13π×32×ha13π×32×hb=21
hahb=21
ha=2hb

Also,
ha+hb=21
2hb+hb=21
3hb=21
hb=7 cm
ha=2×hb=2×7=14 cm

Volume of the remaining part of the cylinder
= Volume of the cylinder - Volume of cone A - Volume of cone B
=πr2h13πr2ha13πr2hb
=(π×32×21)(π3×32×14)(π3×32×7)
=π×9×21π3×9×(14+7)
=(113)×π×9×21
=23×227×9×21
=396 cm3


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