Unit 14 Volume, Sectors and Arcs

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# Unit 14 Volume, Sectors and Arcs - PowerPoint PPT Presentation

Unit 14 Volume, Sectors and Arcs. Unit 14 Volume, Sectors and Arcs. Volume of Cube, Cuboid, Cylinder and Triangular Prism. Cube. Volume = a 3. Cuboid. Volume = abc. Cylinder. Volume = π r 2 h. Triangular Prism. Volume = Al. Volume =. Problem Set & Answers

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### Unit 14Volume, 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 =

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.

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

?

?

?

?

?

?

?

?

### Unit 14Volume, Sectors and Arcs

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Volume of Cube, Cuboid, Cylinder and Triangular Prism

### Unit 14Volume, Sectors and Arcs

Mass, Volume and Density

Note: Density of water = 1 g/cm3

Problem: Find the mass of water in the fish tank

Solution:

Volume,

Mass =

?

?

?

?

### Unit 14Volume, Sectors and Arcs

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Mass, Volume and Density

### 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

### 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

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Volume of Pyramid, Cone and Sphere