Volume of composite solids
To calculate the volume of a composite solid, simply split it into smaller solids and calculate their separate volumes.
The volumes of each of the individual solids are then added together to give the total volume of the composite solid.
Example
Calculate the volume of the solid shown.
Give your answer correct to 2 significant figures.
Answer
Diameter = 10m therefore the radius = \(10 \div 2 = 5\,m\)
Volume of cylinder:
\(V = \pi {r^2}h\)
\(V = \pi \times {5^2} \times 6\)
\(V = 471.238...c{m^3}\)
Volume of sphere:
\(V = \frac{4}{3}\pi {r^3}\)
\(V = \frac{4}{3} \times \pi \times {5^3}\)
\(V = 523.598...c{m^3}\)
Volume of hemisphere \(= 523.598... \div 2 = 261.799...c{m^3}\)
\(Total\,volume = 471.238... + 261.799...\)
\(= 733.037...c{m^3}\)
\(= 730\,c{m^3}(to\,2\,s.f.)\)
More guides on this topic
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- Circle geometry
- Applying Pythagoras Theorem
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates