# Calculating the surface area of the earth essay

Document Type:Essay

Subject Area:Mathematics

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Consequently, I see this internal assessment as an opportunity for me to research into the real size of our beloved planet. I intend to investigate the size of the Earth in terms of the surface area because it is amazing how it can accommodate so many people. According to the current estimates, the surface area of the earth is about 510. 1 million square km using the formula for the surface area of a sphere,. This internal assessment is dedicated to proving the result that has been found for the surface area of the Earth by using the integral calculus. Then, taking the derivative of the equation above: Since the ‘2’ can be simplify each other, it will then be eliminated from the equation: By squaring both sides of the equation, the square root can be eliminated: And hence: By using trigonometric substitution; Let When , When It is then substituted into the equation: is equivalent to , therefore it can be applied to the equation: Which can be simplified, as shown below: Resulting in the equation of the surface area of sphere to be: In calculus, the earth is considered to be a sphere therefore the same formula is used to calculate both its surface area and volume.

Using the formula to calculate the surface area of the earth; Surface area of the earth= The radius, r, of the earth is 6378 Km A= 4*π*6378Km*6378Km Surface Area of the earth= 511,252,214 km2 Surface Area of the earth is therefore 5. 11*108 Km2 As can be deduced, the result of the calculation is not so far from the theoretical surface area of the earth known to be 5. 1*108 Km2 In conclusion, the surface area of the earth has been a very complex calculation given that there has been contention on the shape of the earth. Other methods have been used to calculate the surface area and the result is always almost the same to be about 5. "Calculus II - Surface Area". Tutorial. Math. Lamar.

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