A cylinder is a circular prism. As with other prisms, the volume of a cylinder can be calculated using the cross-sectional area x length.
Th cross-section of a cylinder is a circle. As the area of a circle =`πr^2`, the volume of a cylinder is `πr^2l`, where `r` is the radius of the circular end, and `l` is the length of the cylinder.
1. What is the volume of a cylinder with a diameter of 4cm and a length of 42cm? Give your answer correct to 1 decimal place.
Answer: 527.8 cm3
The radius of a circle is `frac(1)(2)` the diameter = `frac(1)(2) xx 4 = 2`cm
The cross-sectional area is `pir^2 = pi xx 2^2 = 4pi`
The volume of the cylinder = cross-sectional area x volume
`= 4pi xx 42`
= 527.79 cm3
2. What is the diameter of a cylinder with a volume of 1000cm3 and a length of 100cm? Give the answer correct to 1 decimal place.
Volume of a cylinder = `pir^2l`
`1000 = pir^2 xx 100`
`10 = pir^2`
`r^2 = 3.183`
r = 1.784