Question

Earth's radius is approximately 6400 km. What is the surface area & volume of the earth?

Answer 1

Volume V

`V =1.098\ *\ 10^(12)\ km^3`

Surface area
`A_s`

`A_s =5.147\ *\ 10^(8)\ km^2`

Explanation:

Suppose that the shape of the earth is completely spherical.

Then the surface area and the volume of a sphere are given by the following formulas

Surface area
`A_s`

`A_s =4\pi r^2`

Volume V

`V =(4)/(3)\pi r^3`

In this case we know the radius r of the sphere.

`r = 6400\ km`

then we use the radius value to find the volume and surface area

Volume V

`V =(4)/(3)\pi (6400)^3`

`V =1.098\ *\ 10^(12)\ km^3`

Surface area
`A_s`

`A_s =4\pi (6400)^2`

`A_s =5.147\ *\ 10^(8)\ km^2`

Answer 2

`SA=514,457,600\ km^(2)`

`V=1,097,509,546,667\ km^(3)`

Explanation:

step 1

Find the surface area

we know that

the surface area of a sphere is equal to

`SA=4\pi r^(2)`

substitute

`SA=4 \pi (6,400)^(2)`

`SA=163,840,000 \pi\ km^(2)`

substitute the approximate value of pi (3.14)

`SA=(3.14) (163,840,000)`

`SA=514,457,600\ km^(2)`

step 2

Find the volume

The volume is equal to

`V=(4/3)\pi r^(3)`

substitute

`V=(4/3)(3.14) (6,400)^(3)`

`V=1,097,509,546,667\ km^(3)`