Question

assume that the moon is a sphere. what is the volume of the moon if its diameter is 3,476 km? Express your answer in scientific notation to two significant digits.

Answer 1

`V=2.2\ x\ 10^(10) km^3`

Explanation:

The formula to calculate the volume of a sphere is:

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

Where r is the radius of the sphere.

In this case we do not know the radius of the sphere, but we know the diameter.

By definition the diameter of a sphere is equal to twice the radius. This is:

`d = 2r`

`r = (d)/(2)`

In this case d= 3,476 km

So

`r = (3,476)/(2)`

`r = 1738\ km`

Finally

`V=(4)/(3)\pi (1738)^3`

`V=2.20\ x\ 10^(10) km^3`

Answer 2

Volume=2.2*10^10 km^3

Explanation:

Given

Diameter of moon=d=3476 km

The formula for the volume of sphere is:

V=4/3 πr^3

As it can be clearly seen that the formula uses radius, and we are given diameter. So we have to find the radius first

So,

radius=r=d/2

=3476/2

=1738 km

Now putting the value of r and pi in the formula:

V=4/3*3.14*(1738)^3

=12.56/3* 5249879272

= 21979494552.106

Rounded off to two significant digits:

Volume=2.2*10^10 km^3