Answer:
a. The approximate surface area of the Earth based on the diameter of the Earth measured from the poles is approximately 1.961 × 10⁸ mi²
The approximate surface area of the Earth based on the diameter of the Earth measured from the equator is approximately 1.974 × 10⁸ mi²
b. The surface area of the water on Earth using the diameter of the Earth measured from opposite points of the equator is approximately 1.480 × 10⁸ mi²
Step-by-step explanation:
The given parameters are;
The diameter of the Earth measured from the North to the South pole, [tex]D_p[/tex] = 7899.83 miles
The diameter of the Earth measured from (across) opposite points of the equator, [tex]D_e[/tex] = 7926.41 miles
a. The surface area, [tex]A_E[/tex], of the Earth, taking the Earth as a perfect sphere, is given as follows;
A = 4 × π × r²
Where;
r = The radius of the sphere = 1/2 × the diameter of the sphere
For the diameter measured from poles, [tex]r_p[/tex] = [tex]D_p[/tex]/2 = (7899.83 miles)/2 = 3949.915 miles
The approximate surface area of the Earth based on the diameter of the Earth measured from the poles, [tex]A_{Ep}[/tex] = 4 × π × (3949.915 miles)² = 196058359.283 mi² ≈ 1.961 × 10⁸ mi²
For the diameter measured from equator, [tex]r_e[/tex] = [tex]D_e[/tex]/2 = (7926.41 miles)/2 = 3963.205 miles
The approximate surface area of the Earth based on the diameter of the Earth measured from the equator, [tex]A_{Ee}[/tex] = 4 × π × (3963.205 miles)² = 197379906.233 mi² ≈ 1.974 × 10⁸ mi²
b. The percentage of the surface area of the Earth covered by water ≈ 75%
The surface area of water on Earth using the diameter of the Earth = 7926.41 miles (the diameter measured from the equator), we have;
The area of the Earth with a diameter of 7926.41 miles was given as [tex]A_{Ee}[/tex] = 4 × π × ((7926.41 miles)/2)² = 197379906.233 mi²
The surface area of the water on Earth = 75% × The area of the Earth = 75/100 × 197379906.233 = 148034929.675 mi² ≈ 1.480 × 10⁸ mi²
