Question

The radius of the earth is 3963 mi. what is the surface area of the earth in square meters? (1 mi = 1609 m.)'

Answer 1

Surface Area of a Sphere = 4 • π • radius²

Surface Area of a Sphere = 4 * 3.14159 * 3,693*3,693

Surface Area = 171,383,146.70 square miles

1 square mile = 1,609 * 1,609 = 2,588,881 square meters

171,383,146.70 square miles * 2,588,881 = 4.437 x 10^14 square meters

Answer 2

You can think of the earth as almost a sphere(although its not sphere, but a little bit flat at the poles) for this case and then use the formula for finding the surface area of the sphere.

The surface area of the earth in square meters is 510940227330702.3 square meters or $\approx 5.1 \times 10^{14} \: \rm meter^2$

How to find the surface area of a sphere with radius r units?

The surface area of a sphere with radius of r units is

$A_s = 4 \pi r^2 \: \rm unit^2$

Since the radius of the earth is approx 3963 miles, and we have

1 mi = 1609 m approximately, thus,

$3963 \rm \: miles = 3963 \times 1609 = 6,376,467 \: meters$

Thus, surface area of the earth would be approximately

$\text{Surface area of earth} = 4 \times \pi \times (6376467)^2 = 510940227330702.3 \:m^2$

(here we made assumption that earth is perfect sphere with radius 3963 miles which isn't true, so this area is like hypothetical but it gives a rough idea of how big the surface area can be)

Thus,

The surface area of the earth in square meters is 510940227330702.3 square meters approx or $\approx 5.1 \times 10^{14} \: \rm meter^2$

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