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 ${\text{cm}}^3$
• B. 386 ${\text{cm}}^3$
• C. 396 ${\text{cm}}^3$
• D. 406 ${\text{cm}}^3$

Answer 1

The correct option is C

396 ${\text{cm}}^3$

Both cones have congruent bases. So, the radii of the bases will be 3 cm.

Their heights will be 14 cm and 7 cm respectively.

Remaining portion volume = (Volume of cylinder - Volume of two cones)

= $\pi$ $9\times 21$ - $\frac{1}{3}\times 9(14+7)]$

= $\pi$ $\times 9[21-7]$

= $\pi$ $\times 9\times 14$

= $396c{m}^3$