Question

Given that the radius of the sun is approximately `7 xx 10^5` km, what is its approximate volume in cubic kilometres ?

Answer 1

Approximately `1.44 xx 10^18` cubic kilometers.

Explanation:

The volume of a sphere is given by the formula:

`V = 4/3 pi r^3`

If you know that the formula for the surface area of a sphere is:

`S = 4 pi r^2`

then you can derive the formula for the volume by thinking about dissecting the sphere into a large number of tall thin pyramids with base at the surface and vertex at the centre.

The volume of each pyramid is `1/3 xx "base" xx "height"` where the height is the radius of the sphere.

The sum of the base areas of the pyramids is the surface area of the sphere.

Hence the total volume is:

`1/3 S xx r = 1/3 xx 4 pi r^2 xx r = 4/3 pi r^3`

`color(white)()`
In our example, the radius `r` is `7 xx 10^5` km.

So the volume is:

`4/3 pi r^3 = 4/3 pi (7 xx 10^5)^3`

`= 4/3 pi (7^3 xx 10^15)`

`= 4/3 pi xx 343 xx 10^15`

`~~1440 xx 10^15 = 1.44xx 10^18"km"^3`