Question

The adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume of the solid.

Answer 1

Diameter of the cylindrical part =7 cm
Therefore,radius of the cylindrical part = 3.5 cm

Volume of hemisphere$=\frac{2}{3}{\mathrm{\pi r}}^3=\frac{2}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 3.5=89.83{\mathrm{cm}}^3$

Volume of the cylinder$={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times 3.5\times 3.5\times 6.5=250.25{\mathrm{cm}}^3$

Height of cone $=12.8-6.5=6.3cm$

Volume of the cone$=\frac{1}{3}{\mathrm{\pi r}}^{2}h=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 6.3=80.85c{m}^3$

Total volume$=89.83+250.25+80.85=420.93c{m}^3$