The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.
Answers
Given : The diameter of the moon is approximately one fourth of the diameter of the earth.
Let diameter of the earth = d1
Then , diameter of the moon = ¼ d1
Radius of the earth, r1 = d1/2
Radius of the moon ,r2 = d1/2 × 4 = d1/8
We know that, Surface area of the sphere is 4πr² :
Surface area of the earth , S1 = 4πr1²
S1 = 4π(d1/2)²
S1 = 4π × d1²/4
S1 = πd1²
Surface Area of the moon ,S2 = 4π(d1/8)²
S2 = 4π × d1²/64
S2 = πd1²/16
Required Ratio , S1 : S2 = πd1²/1 : πd1²/16
S1(earth) : S2 (moon)= 16 : 1
S2(moon) : S1(earth) = 1 : 16
Hence, the Ratio of their surface areas is 1 : 16.
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Given:-
- The diameter of the moon is approximately one fourth of diameter of earth
To find:-
- find the ratio of their surface areas ..?
Solutions:-
- Let us the diameter of the earth = d km
Therefore,
the radius of the earth = d/2 km
So,
the surface area of the earth = 4πr²
= 4π(d/2)²
= 4πd²/4
Now,
according to the problem, the diameter moon is one fourth of the diameter of earth.
So, the diameter of the moon = d/4 km
Therefore, the. radius of moon = d/8 km
So, the surface area of the moon = 4πr²
= 4π(d/8)²
= 4πd²/64
Ratio of surface = surface area of moon/surface area of earth
= (4πd²/64)/(4πd²/4)
= 4πd²/64 × 4/4πd²
= 4/64
= 1/16
Hence, the ratio of the Surface area of moon to surface area of earth is 1 : 16.
Some Important:-
- The surface area of a sphere = 4πr²
- The curved surface area of hemisphere = 2πr²
- The total surface area of hemisphere = 3πr²
- The volume of the sphere = 4/3 πr²
- The volume of the hemisphere = 2/3 πr²