SOLIDS

1
SOLIDS VOLUME
Common 3D Shapes
sphere
cuboid
cylinder
cube
cone
2
SPHERES
diameter
radius
A sphere is like a circle in 3D so can have a
radius and diameter.
So calculations involving spheres use ?.
It can be shown that the volume occupied/filled
by a sphere is given by the formula
V 4/3?r3
3
Example
12cm
V 4/3?r3
4/3 ?123
4 ? 3 x ? x 12 3
r 12cm
7238.2cm3
4
Example
20m
V 4/3?r3
4/3?103
4 ? 3 x ? x 10 3
4188.8m3
d 20m so r 10m
5
HEMISPHERES
A hemisphere is a half sphere. The equator
divides the earth into the northern southern
hemispheres.
For a sphere we have V 4/3?r3
So for a hemisphere V 2/3?r3
6
Example
An igloo has a diameter of 3m.
Find its volume.
d 3m so r 1.5m
V 2/3?r3
2 ? 3 x ? x 1.5 3
7.069m3