Volume of a cylinder
The formula for the volume of a cylinder (circular prism) is derived from the volume of a prism, where \(r\) is the radius and \(h\) is the height/length.
\(V = Ah\)
Since the area of a circle = \(\pi {r^2}\), then the formula for the volume of a cylinder is:
\(V = \pi {r^2}h\)
Example
Calculate the volume of the cylinder shown.
Give your answer correct to 1 significant figure.
Answer
\(V = \pi {r^2}h\)
\(= \pi \times {4^2} \times 10\)
\(= 502.654...\)
\(= 500\,c{m^3}(to\,1\,s.f.)\)
Now try the example questions below.
Question
Calculate the volume of a cylinder with radius 3.6 cm and height 8.7 cm to the nearest cubic centimetre.
\(V=\pi r^{2}h\)
\(=\pi \times 3.6^{2}\times 8.7\)
\(=354cm^{3}\)
Question
The volume of a cylinder is 198 cm3. If the diameter is 6 cm, calculate the height.
Give your answer correct to the nearest cm.
Diameter = 6cm therefore the radius = \(6 \div 2 = 3\,cm\)
\(V = \pi {r^2}h\)
\(198 = \pi \times {3^2} \times h\)
\(198 = (28.274...) \times h\)
\(h = 198 \div (28.274...)\)
\(h = 7.002...\)
\(h = 7cm\) (to the nearest cm)
More guides on this topic
- Determine the gradient of a straight line
- 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