Proportions to Convert Volume of 2 and 3-d Shapes

Geometric shapes can be 2 dimensional or 3 dimensional.

Two dimensional figures are the figures which are drawn on a 2D plane. Examples for 2 dimensional figures are

• circle
• triangle
  
• rectangle
• square
• pentagon
• hexagon
• septa
  
• octagon etc.

Three dimensional shapes are the shapes which have 3 dimensions like length, width and height. the real life examples a re foot ball, basket ball, bricks etc.

Examples for 3dimensional shapes are:

• sphere
• cube
• cuboid
• prism
• pyramid etc.

Since, the 2D figure have only 2 dimensions, the units for area is unit ² ,and the 3D shapes have 3 dimensions , the units for volume is unit ³

Proportions for 2d figures

before we go for conversion of area of 2D figures, we need to know how the units of length are related.

10 -3 m	mm	Millimeter
10 -2 m	cm	centimeter
10 -1 m	dm	decimeter
10 1 m	dam	decimeter
10 2 m	hm	hectometer
10 3 m	km	kilometer

• When we need to convert the units in to another units then we need identify the conversion factor.
• Multiply the square of the conversion factor with the arae of 2D figure.
• We will get the area in required units.

conversion units

	km	hm	dam	dm	cm	mm
km	1	10	100	10000	100000	1000000
hm	0.1	1	10	1000	10000	100000
dam	0.01	0.1	1	100	1000	10000
dm	0.0001	0.001	0.01	1	10	100
cm	0.00001	0.0001	0.001	0.1	1	10
mm	0.000001	0.00001	0.0001	0.01	0.1

Example:

Area of a rectangle is 30 cm ², convert it in to decimeters.

solution:

From the table, conversion factor is 1 cm=0.1dm

so, area in dm= 30 x (0.1 dm) ²

=30 x 0.01 dm ²

=0.3 dm ²

Example 2:

Area of a rectangle is 300 cm ², convert it in to meters.

Solution:

From the table, conversion factor is 1 cm=0.01m

so, area in dm= 300 x (0.01 m) ²

=300 x 0.0001 m ²

=.003 m ²