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
Unit 14
Volume, Sectors and Arcs
Volume of Cube, Cuboid, Cylinder
and Triangular Prism
Cube
Volume = a3
Cuboid
Volume = abc
Cylinder
Volume = πr2h
Triangular Prism
Volume = Al
Volume =
Problem Set & Answers
a) What is the area, in cm2, of the base of the tank?
Area of base =
?
?
h
?
40cm
Water is poured into the tank, to a height of 15 cm.
75cm
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
?
?
?
?
?
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
Unit 14
Volume, Sectors and Arcs
Mass, Volume and Density
Mass
=
Volume
=
Density
=
Problem: Find the mass of water in the fish tank
Solution:
Volume,
?
?
?
Mass =
?
Note: Density of water = 1 g/cm3
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
Unit 14
Volume, Sectors and Arcs
Sector Area and Arc Length
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:
Arc Length
?
Example
Arc length
?
?
?
?
?
Sector Area
Area of Sector
?
Example
Sector Area, A
?
?
?
?
?
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
Unit 14
Volume, Sectors and Arcs
Volume of Pyramid, Cone and
Sphere
Pyramid
Cone
Sphere
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,
?
?
?
?
?
?
?
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