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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.

2d figures

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

kmhmdamdmcmmm
km110100100001000001000000
hm0.1110100010000100000
dam0.010.11100100010000
dm0.00010.0010.01110100
cm0.000010.00010.0010.1110
mm0.0000010.000010.00010.010.1

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