The diameter of the moon is approx. One-fourth the diameter of the earth. Find the ratio of their surface area.
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Let the diameter of earth be x
Then diameter of moon = 1/4 of x = x/4
Radius of earth = x/2
Radius of moon = (x/4)/2 = x/8
Surface area of earth = 4πr²
= 4π (x/2)²
= 4π (x²/4)
= πx²
Surface area of moon = 4πr²
= 4π (x/8)²
= 4π (x²/64)
= πx²/16
Ratio of the surface areas of the earth and moon = πx² : πx²/16
= πx²/πx² : 16/1
= 1 : 16
∴ The ratio = 1:16
Then diameter of moon = 1/4 of x = x/4
Radius of earth = x/2
Radius of moon = (x/4)/2 = x/8
Surface area of earth = 4πr²
= 4π (x/2)²
= 4π (x²/4)
= πx²
Surface area of moon = 4πr²
= 4π (x/8)²
= 4π (x²/64)
= πx²/16
Ratio of the surface areas of the earth and moon = πx² : πx²/16
= πx²/πx² : 16/1
= 1 : 16
∴ The ratio = 1:16
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