This document contains 4 presentations on volume, sectors, and arcs. The first presentation defines the formulas for calculating the volumes of cubes, cuboids, cylinders, and triangular prisms. The second presentation covers the relationships between mass, volume, and density. The third presentation provides the formulas for finding the areas of sectors and arc lengths of circles. The final presentation defines the volume formulas for pyramids, cones, and spheres and includes an example problem calculating the height of a cone with the same volume and radius as a sphere.

1. Unit 14
Volume, Sectors and Arcs
Presentation 1 Volume of Cube, Cuboid, Cylinder and Triangular Prism
Presentation 2 Mass, Volume and Density
Presentation 3 Sector Area and Arc Length
Presentation 4 Volume of Pyramid, Cone and Sphere

2. Unit 14
Volume, Sectors and Arcs
Volume of Cube, Cuboid, Cylinder
and Triangular Prism

3. Cube
Volume = a3Volume = a3

4. Cuboid
Volume = abcVolume = abc

5. Cylinder
Volume = πr2
hVolume = πr2
h

6. Triangular Prism
Volume = AlVolume = Al
Volume =Volume =

7. Water is poured into the tank, to a height of 15 cm.
b) Calculate, in cm3
, the volume of water in the tank.
Volume =
c) If the tank holds 84 litres when full, calculate the height, h, in cm, of water
when the tank is full.
When full, the tank holds 84 x 1000cm3
of water,
so
75cm
40cm
h
Problem Set & Answers
a) What is the area, in cm2
, of the base of the
tank?
Area of base =
?? ?? ??
?? ?? ??
??
??
??
????

8. Unit 14
Volume, Sectors and Arcs
You have finished viewing:
Volume of Cube, Cuboid, Cylinder and
Triangular Prism
Return to front slide
Presentation 1 Volume of Cube, Cuboid, Cylinder and Triangular Prism
Presentation 2 Mass, Volume and Density
Presentation 3 Sector Area and Arc Length
Presentation 4 Volume of Pyramid, Cone and Sphere

9. Unit 14
Volume, Sectors and Arcs
Mass, Volume and Density

10. Mass =
Volume =
Density =
Note: Density of water = 1 g/cm3
Problem: Find the mass of water in the fish tank
Solution:
Volume,
Mass =
??
??
??
??

11. Unit 14
Volume, Sectors and Arcs
You have finished viewing:
Mass, Volume and Density
Return to front slide
Presentation 1 Volume of Cube, Cuboid, Cylinder and
Triangular Prism
Presentation 2 Mass, Volume and Density
Presentation 3 Sector Area and Arc Length
Presentation 4 Volume of Pyramid, Cone and Sphere

12. Unit 14
Volume, Sectors and Arcs
Sector Area and Arc Length

13. Arc Length
If the angle subtended by the arc at the centre
of the circle is θo
, then the arc length, l, is
given by:
Example
Arc length
??
??
??
??
??
??
Arc Length

14. Sector Area
Example
Sector Area, A
??
??
??
??
??
??
Area of Sector

15. Unit 14
Volume, Sectors and Arcs
You have finished viewing:
Sector Area and Arc Length
Return to front slide
Presentation 1 Volume of Cube, Cuboid, Cylinder and
Triangular Prism
Presentation 2 Mass, Volume and Density
Presentation 3 Sector Area and Arc Length
Presentation 4 Volume of Pyramid, Cone and Sphere

16. Unit 14
Volume, Sectors and Arcs
Volume of Pyramid, Cone and
Sphere

17. Pyramid
Cone
Sphere

18. Problem
A cone and sphere have the same radius of 12 cm.
If the cone and sphere have the same volume, find the height of the
cone.
Solution
If height of cone is h, then
Volume of cone
Volume of sphere
As the volumes are equal,
????
????
?? ??
??
??
??

19. Unit 14
Volume, Sectors and Arcs
You have finished viewing:
Volume of Pyramid, Cone and Sphere
Return to front slide
Presentation 1 Volume of Cube, Cuboid, Cylinder and
Triangular Prism
Presentation 2 Mass, Volume and Density
Presentation 3 Sector Area and Arc Length
Presentation 4 Volume of Pyramid, Cone and Sphere