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# 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