The diameter of the moon is approximately one fourth of the diameter of the earth.Find the ratio of their surface areas.
Question
The diameter of the moon is approximately one fourth of the diameter of the earth.Find the ratio of their surface areas.
Solution
The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere.
Step 1: Given that the diameter of the moon is one fourth of the diameter of the earth, the radius of the moon is also one fourth of the radius of the earth. Let's denote the radius of the earth as R. Then the radius of the moon is R/4.
Step 2: The surface area of the earth is 4πR² and the surface area of the moon is 4π(R/4)².
Step 3: To find the ratio of their surface areas, we divide the surface area of the moon by the surface area of the earth.
This gives us [4π(R/4)²] / [4πR²] = (R/4)² / R² = 1/16.
So, the ratio of the surface area of the moon to the surface area of the earth is 1:16.
Similar Questions
The ratio of the lengths of corresponding parts in two similar solids is 4:1. What is the ratio of their surface areas?A.16:1B.4:1C.8:1D.64:1
Calculate the surface area to volume ratio of the following shape. The volume is 4 cm3 and the surface area is 18 cm2. Use a calculator if required.
The Moon is approximately at a distance of from the Earth. The Earth is approximately wide.How many Earths can we fit in the space between the Earth and the Moon?
If the surface areas of two spheres are in the ratio of 4 : 25, then the ratio of their volumes is
The ratio of the surface areas of two similar solids is 16:144. What is the ratio of their corresponding side lengths?A.4:12B.4:C.:12D.1:96
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.