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

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Volume of Cube, Cuboid, Cylinder and Triangular Prism

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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

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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