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# surface area of sphere: investigation

Module by: Anthony Padayachee. E-mail the author

Investigation: To find the level of correlation between the formula for the surface area of a sphere and the practical calculation of surface area of a soccer ball.

1. The Surface Area of a Sphere

Formula: Surface Area = 4 π r2r2r^2

2. Formula for Area of triangle

3.      The cosine rule

Information:

The soccer ball comprises of 20 regular hexagons and 12 regular pentagons. These are arranged in a specific format to create the sphere,

Measurements taken revealed the following:

The sides of the hexagon and the pentagon measure 42mm.

The diameter of the ball is 204mm,

Use these dimensions to verify the formulae.

You are expected to find the sum of the the areas of the hexagons and the pentagons and then compute the surface area of the ball using the formula. You need to then compare the the answers and provide suitable explanations if there are variations in the answers.

Solutions:

Area of a hexagon= 4581.1

Area of a pentagon = 3036.7

Therefore the total surface area = 12(3036.7) + 20(4581.1)

= 128062.4 sq mm

Using the formula,

Surface Area = 4 π r2r2r^2

= 130740.5 sq mm

There is a difference of 2678.1 sq mm. This difference could have resulted from the measurements being inaccurate or from the fact that the actual surface of the ball is a curve, which would have resulted in a slightly higher value for the area than that given by the planar area formulae.

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