Volume of a cone
The volume of a cone is \(\frac{1}{3}\) of the volume of a cylinder with the same area.
The formula for calculating the volume of a cone, where r is the radius and h is the perpendicular height is:
\(V = \frac{1}{3}\pi {r^2}h\)
Example
Calculate the volume of a cone with radius 5cm and height 12cm.
Answer
\(V = \frac{1}{3}\pi {r^2}h\)
\(= \frac{1}{3} \times \pi \times {5^2} \times 12\)
\(= 314.159...\)
\(= 314.16\,c{m^3}(to\,2\,d.p.)\)
Question
Calculate the volume of a cone with radius 2.7 cm and height 9.2 cm to one decimal place.
\(v=\frac{1}{3}\pi r^{2}h\)
\(=\frac{1}{3}\times \pi \times 2.7^{2}\times 9.2\)
\(=70.2cm^{3}\)
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