In this time, we will prove the surface area formula of a sphere. Surface area is the area of the outer part of an object. It is basically the sum of all the areas of all the shapes that cover the surface of the object.
We use a ball with patterns of hexagon and pentagon on it (soccer/futsal ball). We use two ways to count the surface area of the ball, the first way is by counting the area of all of the hexagon and pentagon and then add it, and the second way is by counting it using the sphere surface area formula.
1st way:
Count the total area of pentagon and the total area of hexagon. After that, sum up the total area of pentagon and the total area of hexagon.
a: length of side (3.5 cm)
Area of pentagon: 
= 21.08 cm²
Area of hexagon: 
= 31.83 cm²
Total area of pentagon (there are 12 pentagons): 21.08 × 12 = 252.96 cm²
Total area of hexagon (there are 20 hexagons): 31.83 × 20 = 636.6 cm²
Surface area of sphere: 252.96 + 636.6 = 889.56 cm²
From the first way, we found out that the surface area of the ball is 889.56 cm²
2nd way:
Count it using the sphere surface area formula
r: radius (8.5 cm)
Sphere surface area: 4πr² = 907.92 cm²
From the second way, we found out that the surface area of the ball is 907.92 cm²
From the two ways, we see that it shows different results but the numbers are quite near to each other. This is maybe because the surface of the sphere is not flat, so we don’t get the actual number of the length of the sides (for the 1st way) or the radius of the ball (for the 2nd way).
Overall from this activity, I now know the way to count the surface area of a sphere.
MATH IS FUN! 