Unit 14 Volume, Sectors and Arcs Presentation 1Volume of Cube, Cuboid, Cylinder and Triangular Prism...
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Transcript of Unit 14 Volume, Sectors and Arcs Presentation 1Volume of Cube, Cuboid, Cylinder and Triangular Prism...
Unit 14Volume, 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 14Volume, Sectors and Arcs
Volume of Cube, Cuboid, Cylinder and Triangular Prism
Cube
Volume = a3Volume = a3
Cuboid
Volume = abcVolume = abc
Cylinder
Volume = πr2hVolume = πr2h
Triangular Prism
Volume = AlVolume = Al
Volume = Volume =
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
75cm40cm
h
Problem Set & Answers
a) What is the area, in cm2, of the base of the tank?
Area of base = ?? ?? ??
?? ?? ??
????
??????
Unit 14Volume, 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 14Volume, Sectors and Arcs
Mass, Volume and Density
Mass =
Volume =
Density =
Note: Density of water = 1 g/cm3Problem: Find the mass of water in the fish tank
Solution:
Volume,
Mass =
??
????
??
Unit 14Volume, 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 14Volume, 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:
Example
Arc length
??
????
??
????
Arc Length
Sector Area
Example
Sector Area, A
??
????
????
??
Area of Sector
Unit 14Volume, 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 14Volume, 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 14Volume, 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