1. Volumes Of Solids. 8m 5m
7cm
5 cm
14cm
6cm
4cm
4cm
3cm
12 cm
10cm

2. What Is Volume ?
The volume of a solid is the amount of space inside the solid.
Consider the cylinder below:
If we were to fill the cylinder with water the volume would be the amount of water the cylinder could hold:

3. Measuring Volume. Volume is measured in cubic units.
Here is a cubic centimeter
It is a cube which measures 1cm in all directions.
1cm
We will now see how to calculate the volume of various shapes.

4. Volumes Of Prisms. Look at the rectangular prism below: 4cm 3cm 10cm
We must first calculate the area of the base of the rectangular prism:
The base is a rectangle measuring 10cm by 3cm:
3cm
10cm

5. 3cm
10cm
Area of a rectangle = base x height
Area = 10 x 3
Area = 30cm2
We now know we can place 30 centimeter squares on the base of the rectangular prism. But we can also place 30 cubic centimeters on the base to fill the prism:
10cm
3cm
4cm

6. 10cm
3cm
4cm
We have now have to find how many layers of 1cm cubes we can place in the rectangular prism:
We can fit in 4 layers.
Volume = 30 x 4
Volume = 120cm3
That means that we can place 120 of our cubes measuring a centimeters in all directions inside our rectangular prism.

7. 10cm
3cm
4cm
We have found that the volume of the rectangular prism is given by:
Volume = 10 x 3 x 4 = 120cm3
This gives us our formula for the volume of a cuboid:
Volume = Area of the Base X Height
V=Bh for short.

8. The Volume Of A Cylinder.
Consider the cylinder below:
It has a height of 6cm .
4cm
6cm
What is the size of the radius ?
2cm
Volume = Area of base x height
What shape is the base?
Circle
Calculate the area of the base:
A =  r 2
A = 3.14 x 2 x 2
The formula for the volume of a cylinder is:
V = Bh
B = area of the base ( r 2)
h = height.
A = cm2
Calculate the volume:
V =  r 2 x h
V = x 6
V75.36 cm3

9. Volume Of A Cone. Consider the cylinder and cone shown below: D
The diameter (D) of the top of the cone and the cylinder are equal. H
The height (H) of the cone and the cylinder are equal.
If you filled the cone with water and emptied it into the cylinder, how many times would you have to fill the cone to completely fill the cylinder to the top ?
This shows that the cylinder has three times the volume of a cone with the same height and radius.
3 times.

10. The experiment on the previous slide allows us to work out the formula for the volume of a cone:
The formula for the volume of a cylinder is :
V = Bh
We have seen that the volume of a cylinder is three times more than that of a cone with the same diameter and height .
The formula for the volume of a cone is: h r
B= area of the base
h = height

11. Calculate the volume of the cones below:
(2) 9m 6m
(1)

12. Spheres
Definition:
In space, the set of all points that are a given distance from a given point, called the center.
A sphere is formed by revolving a circle about its diameter.

13. Volume of Sphere Volume (V) = Volume= 2304π cm3  7238.23 cm3 r 12 cm
Example:
Find the surface area and volume of the sphere.
Volume= 2304π cm3  cm3