Worked example
Calculate the volume of the solid shown.
First break the composite solid down into basic solids - in this case a cylinder and a hemisphere (half of a sphere).
The volume of the cylinder \(= \pi {r^2}h\)
\(= \pi \times {5^2} \times 6\) (r = 5m since diameter = 10m)
\(= 471.24m^{3}\,(to\,2\,d.p.)\)
Volume of the sphere \(= \frac{4}{3}\pi {r^3}\).
(To work out the volume of the hemisphere we work out the volume of the sphere first then divide it by 2).
\(= \frac{4}{3} \times \pi \times {5^3}\)
\(= 523.599{m^3}\)
Volume of hemisphere \(= 523.599 \div 2 = 261.8{m^3}\)
Now add together the volumes of the cylinder and the hemisphere.
\(471.2 + 261.8 = 733.0{m^3}\)
Total volume of composite solid \(= 733.0{m^3}\)
Now try this question
Question
Calculate the volume of this solid.
This solid is made up of a cylinder and a hemisphere.
Volume of cylinder\(=\pi\,r^{2}h\)
The radius of the circle is half of \(31.8cm\) which is \(15.9cm\).
Volume of cylinder \(=\pi\times15.9\times15.9\times21.5=17067.2\,cm^{3} \)
Volume of sphere \( =\frac{4}{3}\times\pi\times15.9\times15.9\times15.9=16829.1\,cm^{3} \)
Volume of hemisphere \( =\frac{1}{2}\times16829.1=8414.5cm^{3}\)
Total volume of solid \(=17067.2+8414.5=25481.7\,cm^{3}\)
