the diameter of the moon is approximately one-fourth of the diameter of the earth find the ratio of their surfaces Related: Volume of Sphere and Hemisphere(Sphere With Examples)?

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the diameter of the moon is approximately one-fourth of the diameter of the earth find the ratio of their surfaces Related:  Volume of Sphere and Hemisphere(Sphere With Examples)?

Answer

Answer

Answer

The Ratio of the Surfaces of the Moon and Earth

The diameter of the moon is approximately one-fourth of the diameter of the earth. We can use this information to find the ratio of their surfaces.

Surface Area of a Sphere
To find the surface area of a sphere, we use the formula:

Surface Area = 4πr²

Where π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.

Relationship between Diameter and Radius
The radius of a sphere is half of its diameter. So, if the diameter of the moon is one-fourth of the diameter of the earth, then the radius of the moon is also one-fourth of the radius of the earth.

Calculating the Ratio of the Surfaces
Let's assume the diameter of the earth is D. Therefore, the diameter of the moon is D/4.

The radius of the earth is D/2, and the radius of the moon is (D/4)/2 = D/8.

Now, let's calculate the surface area of the earth and the moon.

Surface Area of Earth = 4π(D/2)² = 4π(D²/4) = πD²

Surface Area of Moon = 4π(D/8)² = 4π(D²/64) = πD²/16

Ratio of the Surfaces
To find the ratio of the surfaces, we divide the surface area of the moon by the surface area of the earth:

Ratio = (Surface Area of Moon) / (Surface Area of Earth)
= (πD²/16) / (πD²)
= 1/16

Therefore, the ratio of the surfaces of the moon and earth is 1/16.

Summary:
- The ratio of the surfaces of the moon and earth is 1/16.
- The diameter of the moon is one-fourth of the diameter of the earth.
- We can calculate the surface area of a sphere using the formula: Surface Area = 4πr², where r is the radius of the sphere.
- The radius of the moon is one-fourth of the radius of the earth.
- By substituting the values into the surface area formula, we can find the surface area of the moon and earth.
- Dividing the surface area of the moon by the surface area of the earth gives us the ratio of their surfaces.

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