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the diameter of the moon is approximately one fourth of the diameter of the earth.find the ratio of their surface areas.
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Diameter of the Moon and Earth
To find the ratio of the surface areas of the moon and the earth, we first need to understand the relationship between their diameters. It is given that the diameter of the moon is approximately one-fourth of the diameter of the earth.
Calculating the Ratio of Surface Areas
The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius of the sphere. Since we know the diameter of the moon is one-fourth of the diameter of the earth, we can say that the radius of the moon is also one-fourth the radius of the earth.
Let's assume the radius of the earth is R. Therefore, the radius of the moon will be R/4.
Calculating the Surface Area of the Earth
The surface area of the earth can be calculated using the formula A = 4πR^2, where R is the radius of the earth.
Calculating the Surface Area of the Moon
The surface area of the moon can be calculated using the formula A = 4π(R/4)^2. We substitute R/4 for the radius of the moon.
Expressing the Ratio of Surface Areas
Now, let's calculate the ratio of the surface areas of the moon and the earth.
Ratio = Surface Area of Moon / Surface Area of Earth
Ratio = (4π(R/4)^2) / (4πR^2)
Simplifying the equation, we get:
Ratio = (R^2/16R^2) = 1/16
Therefore, the ratio of the surface areas of the moon and the earth is 1/16.
Conclusion
The ratio of the surface areas of the moon and the earth is 1/16. This means that the surface area of the moon is 1/16th of the surface area of the earth.
To find the ratio of the surface areas of the moon and the earth, we first need to understand the relationship between their diameters. It is given that the diameter of the moon is approximately one-fourth of the diameter of the earth.
Calculating the Ratio of Surface Areas
The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius of the sphere. Since we know the diameter of the moon is one-fourth of the diameter of the earth, we can say that the radius of the moon is also one-fourth the radius of the earth.
Let's assume the radius of the earth is R. Therefore, the radius of the moon will be R/4.
Calculating the Surface Area of the Earth
The surface area of the earth can be calculated using the formula A = 4πR^2, where R is the radius of the earth.
Calculating the Surface Area of the Moon
The surface area of the moon can be calculated using the formula A = 4π(R/4)^2. We substitute R/4 for the radius of the moon.
Expressing the Ratio of Surface Areas
Now, let's calculate the ratio of the surface areas of the moon and the earth.
Ratio = Surface Area of Moon / Surface Area of Earth
Ratio = (4π(R/4)^2) / (4πR^2)
Simplifying the equation, we get:
Ratio = (R^2/16R^2) = 1/16
Therefore, the ratio of the surface areas of the moon and the earth is 1/16.
Conclusion
The ratio of the surface areas of the moon and the earth is 1/16. This means that the surface area of the moon is 1/16th of the surface area of the earth.
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