The diameter of moon is approximately one-fourth of the diameter of the earth. Find theratio of their surface areas.

Sure, let's solve this step by step.

Step 1: Understand the problem The problem states that the diameter of the moon is one-fourth the diameter of the earth. We are asked to find the ratio of their surface areas.

Step 2: Recall the formula for the surface area of a sphere The formula for the surface area of a sphere is 4πr², where r is the radius of the sphere.

Step 3: Understand that the ratio of the diameters is the same as the ratio of the radii Since the diameter is twice the radius, the ratio of the diameters of the moon and the earth is the same as the ratio of their radii.

Step 4: Use the ratio of the radii to find the ratio of the surface areas The ratio of the radii is 1:4 (moon:earth). Since the surface area is proportional to the square of the radius, the ratio of the surface areas is (1²):(4²) = 1:16.

So, the ratio of the surface areas of the moon to the earth is 1:16.