two solid cones A and B are placed in acylindrical tube the ratio of their capacities are 2:1 - Maths - Surface Areas and Volumes

Question

two solid cones A and B are placed in acylindrical tube the
ratio of their capacities are 2:1 find the heights and capacities
of cones also find the volume of the remaining portion of the
cylinder

ramandeep.singh · Accepted Answer

$\frac{V_{A}}{V_{B}} = \frac{2}{1} \Rightarrow \frac{\frac{1}{3} π r^{2} h}{\frac{1}{3} π r^{2} (21 cm - h)} = \frac{2}{1} \Rightarrow h = 42 cm - 2 h ∴ h = 14 cm$

$∴ V_{A} = \frac{1}{3} π r^{2} h = \frac{1}{3} \times \frac{22}{7} \times (3)^{2} \times 14 c m^{3} = 132 c m^{3} V_{B} = \frac{1}{3} π r^{2} (21 - h) = \frac{1}{3} \times \frac{22}{7} \times (3)^{2} \times (21 - 14) c m^{3} = 66 c m^{3}$

Remaining volume = $[π (3)^{2} (21) - 132 - 66] c m^{3}$

= $396 c m^{3}$

two solid cones A and B are placed in acylindrical tube. the ratio of their capacities are 2:1. find the heights and capacities of cones. also find the volume of the remaining portion of the cylinder.