Math, asked by john6066, 9 months ago

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Answers

Answered by nikitasingh79

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.

HOPE THIS ANSWER WILL HELP YOU…..

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

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