Math unit14 volumes

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


Volume of Cube, Cuboid, Cylinder and Triangular Prism

Cube

Volume = a3

Cuboid

Volume = abc

Cylinder

Volume = πr2h

Triangular Prism

Volume = Al

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 = ? ? ?

? ? ?

??

???


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Volume of Cube, Cuboid, Cylinder and Triangular Prism

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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 =

?

??

?



Mass, Volume and Density







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



Sector Area and Arc Length







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,

??

??

? ?

??

?



Volume of Pyramid, Cone and Sphere






Math unit14 volumes

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