Question

4.8 surface area and volume of spheres
the moons radius is about 1080 miles. the earths radius is about 3960 miles. find the surface area of the earth and the surface area of the moon. use 3.14 for pi.
moons radius: about 1080 miles
earths radius: about 3960 miles
surface area of earth =
mi²
surface area of moon =
mi²

Explanation:

Step1: Recall surface - area formula for sphere

The surface - area formula of a sphere is $A = 4\pi r^{2}$, where $r$ is the radius of the sphere.

Step2: Calculate Earth's surface area

Given $r_{Earth}=3960$ miles and $\pi = 3.14$. Substitute into the formula: $A_{Earth}=4\times3.14\times3960^{2}$. First, calculate $3960^{2}=3960\times3960 = 15681600$. Then, $4\times3.14\times15681600=4\times49240224 = 196960896$ square miles.

Step3: Calculate Moon's surface area

Given $r_{Moon}=1080$ miles and $\pi = 3.14$. Substitute into the formula: $A_{Moon}=4\times3.14\times1080^{2}$. First, calculate $1080^{2}=1080\times1080 = 1166400$. Then, $4\times3.14\times1166400=4\times3662496 = 14649984$ square miles.

Answer:

surface area of earth = $196960896$ mi²
surface area of moon = $14649984$ mi²