Surface Area and Radius Relationships

The session discusses a problem involving the diameters of the Moon and Earth, focusing on finding the ratio of their surface areas. It explains the formula for the surface area of a sphere and calculates the radii of both celestial bodies. The solution involves calculating the surface areas and determining the ratio, which is found to be 1:16. The session concludes with a summary of the findings.

What is the relationship between the diameters of the Moon and the Earth as given in the problem?

• The Moon's diameter is one-fourth of the Earth's diameter.

• The Moon's diameter is one-third of the Earth's diameter.

• The Moon's diameter is equal to the Earth's diameter.

• The Moon's diameter is half of the Earth's diameter.

What is the formula for the surface area of a sphere?

• πr²

• 3πr²

• 4πr²

• 2πr²

If the diameter of the Earth is D, what is the radius of the Earth?

• D/8

• D/2

• D/4

• D

How is the radius of the Moon calculated if its diameter is D/4?

• D/16

• D/4

• D/8

• D/2

What is the surface area of the Moon if its radius is D/8?

• 4π(D²/16)

• 4π(D²/64)

• 4π(D²/8)

• 4π(D²/4)

What is the surface area of the Earth if its radius is D/2?

• 4π(D²/4)

• 4π(D²/16)

• 4π(D²/64)

• 4π(D²/8)

What is the ratio of the surface areas of the Moon to the Earth?

• 1:8

• 1:16

• 1:4

• 1:32

Which mathematical operation is used to simplify the ratio of the surface areas?

• Addition

• Multiplication

• Division

• Subtraction

What happens to the π terms when calculating the ratio of the surface areas?

• They are added together.

• They cancel each other out.

• They remain unchanged.

• They are multiplied.

What is the final step in finding the ratio of the surface areas?

• Subtracting the surface areas.

• Adding the surface areas.

• Dividing the surface areas.

• Multiplying the surface areas.