Ratio of the Surface Areas of the Moon and Earth

To find the ratio of the surface areas of the Moon and Earth, we first need to determine the surface areas of each celestial body. Since we are given that the diameter of the Moon is approximately one fourth of the diameter of the Earth, we can use this information to calculate their respective surface areas.

Calculating the Surface Area of the Moon
1. The diameter of the Moon is one fourth of the diameter of the Earth, which means the radius of the Moon is also one fourth of the radius of the Earth.
2. Since the formula for the surface area of a sphere is 4πr^2, we can substitute the radius of the Moon into this formula to find its surface area.
3. Let's assume the radius of the Earth is 'R'. Therefore, the radius of the Moon would be 'R/4'.
4. Plugging the value of the radius into the formula, we get the surface area of the Moon as 4π(R/4)^2 = πR^2/4.

Calculating the Surface Area of the Earth
1. We know the formula for the surface area of a sphere is 4πr^2.
2. Let's assume the radius of the Earth is 'R'.
3. Plugging the value of the radius into the formula, we get the surface area of the Earth as 4πR^2.

Calculating the Ratio of Surface Areas
1. Now that we have the surface areas of both the Moon and Earth, we can calculate their ratio.
2. Ratio = Surface Area of the Moon / Surface Area of the Earth.
3. Substituting the values we obtained earlier, the ratio becomes (πR^2/4) / (4πR^2).
4. Simplifying further, the ratio becomes 1/16.

Conclusion
The ratio of the surface areas of the Moon and Earth is 1/16. This means that the surface area of the Moon is 1/16th of the surface area of the Earth.