8.07 Volume of cylinders and spheres (Extended)
Volume of a cylinder
A cylinder is very similar to a prism, other than having a rounded face. The volume can be found using the same process that we have learnt for prisms.
To determine the volume of a cylinder we need the radius (or diameter) to calculate the area of the round base and the height (or length) of the cylinder.
| $\text{Volume of cylinder }$Volume of cylinder | $=$= | $\text{area of base }\times\text{height }$area of base ×height |
| $=$= | $\pi r^2\times h$πr2×h |
Practice questions
QUESTION 1
The volume of a cylinder is given by $V=\pi r^2h$V=πr2h.
Find the volume of the cylinder shown, rounding your answer to two decimal places.
QUESTION 2
Find the volume of a cylinder correct to one decimal place if its diameter is $2$2 cm and its height is $19$19 cm.
QUESTION 3
If the radius of a cylinder is $8$8 cm and its height is $18$18 cm, find the amount of water it can hold in litres, correct to two decimal places.
Volume of a sphere
A sphere is defined as the collection of points that are all equal distance from the centre of the sphere. The distance from the centre is the radius of the sphere.
The volume of a sphere with radius $r$r can be calculated using the following formula.
$\text{Volume of sphere }=\frac{4}{3}\pi r^3$Volume of sphere =43πr3
Practice questions
question 4
Find the volume of the sphere shown.
Round your answer to two decimal places.
question 5
The radius of a bowling ball is $10.9$10.9 cm; what is its volume?
Round your answer to three decimal places.