Question

the diameter of the moon is approximately one fourth of diameter of earth find the ratio of their surface areas ​

Answer 1

Answer:

4:1 diameter

area 16:1

square of d

Answer 2

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