# Area and Volume

## Perimeter

Perimeter = distance around the edge.

You could walk around the perimeter.

### All dimensions must have the same units !

Don't mix cm with m.

### Perimeter has plain units.

Example

P = 5 + 2 + 2 + 3 + 9 + 3 + 2 + 2 cm
P = 28 cm

## Area

Area = floor space covered

You could paint an area.

### All dimensions must have the same units !

Don't mix cm,2 with m2

1 m2 = 100cm x 100cm

= 10000 cm2

### Area of a square

Example

Calculate the area of the square

### Area of a rectangle

Examples

Calculate the area of the rectangles

### Area of a triangle

Area of a triangle = ½ x base x perpendicular height

Examples

Find the area of the triangle below:

What is the length of the base of the triangle, if it has an area of 45 cm2 ?

### Area of kite

Example

Calculate the area of the following kite:

### Area of Trapezium

Area of a trapezium = ½ x average of base x perpendicular height

Example

What is the area of this trapezium ?
(Each square represents 1 cm2 )

### Area of a parallelogram

Example

Calculate the area of the parallelogram :

### Area of a rhombus

Example

Calculate the area of the rhombus:

( The sizes are for the complete diagonals)

## Volume

Volume = capacity held

You could fill a volume

### All dimensions must have the same units !

Don't mix cm with m.

### Volume  has  units3

Notice that for a cuboid

Example

Calculate the volume of the cuboid below:

Example

Converting 1m3 to litres

First, convert the units

But 1 cm3 = 1 ml and 1000 ml = 1litre
Divide cm3 by 1000 for litres.

So  1 000 000 cm3 = 1000 litres
1 m3 = 1000 litres

## Volume of a Sphere

A sphere has volume

Where r is the radius of the sphere.

Examples

Calculate the volume of the following sphere.
Give your answer correct to 1 dp and also to 2 sig figs.

Calculate the volume of the following sphere.

Calculate the diameter of a sphere which has a volume of 700cm3.

## Volume of a Cone

A cone has volume

Where r is the radius of the circular part of the cone  and h is the perpendicular height of the cone.

Example
Calculate the volume of an ice cream cone which has a diameter of 4cm and a height of 6cm. Give your answer correct to 1 dp.

How many of these cones can be filled from 1litre of ice cream ?
1000 cm3 = 1 l

1000 ÷ 25.1 = 39.84
So 39 cones can be filled from one litre of ice cream.

Example
Calculate the height an ice cream cone which has a diameter of 4cm and a volume of 35ml. Give your answer correct to 1 dp.

The cone is 8.4 cm tall.

Example
Calculate the diameter of an ice cream cone which has a height of 8cm and a volume of 90ml. Give your answer correct to 1 dp.

## Volume of a prism

For a prism,  V=Ah

So Volume = Area x height   (or Area x Length if laying down)

Example

What is the volume of  a prism which has an area of 37 cm2    and a height of 4 cm ?

## Volume of a cylinder

A cylinder is a circular prism,

Example

Calculate the volume of a tin can which has a height of 0.8m and a diameter of 10 cm. Give your answer correct to 1 sigfig.

Example
Calculate the diameter of a tin can which has a height of 8cm and a volume of 90ml. Give your answer correct to 1 dp.

## Volume of a pyramid

The volume of any pyramid is given as

where A is the area of the base of the pyramid and h is its height.

Examples

What is the volume of this squared based pyramid ?

What is the volume of this rectangular based pyramid ?

What is the volume of this triangular based pyramid ?

## Surface area

The surface area is the total external area
of the shape.

Example

Find the surface area of the cuboid :

This shape has 6 faces

2 faces have area    6cm x 4cm
2 faces have area    6cm x 2cm
2 faces have area    2cm x 4cm

2 x 6cm x 4cm =  48 cm2
2 x 6cm x 2cm =  24 cm2
2 x 2cm x 4cm =  16  cm2
Surface Area =   88  cm2

Surface Area ≠Volume

## Composite area

Cut into convenient shapes
Find missing dimensions
Calculate individual areas
Calculate  total

Remember
all dimensions must have the same units !

Example

A shape = A 1 + A 2
A 1 = 5x2 = 10 cm2
A 2 = 3x9 = 27 cm2
A shape = 37 cm2

## Composite Volume

Cut into convenient shapes
Find missing dimensions
Calculate individual areas
Calculate  total

Example