Question

The circumference of an NBA-approved basketball is 29.6 in. Given that the radius of Earth is about 6400 km, how many basketballs would it take to circle around the equator with the basketballs touching one another? Round off your answer to an integer with three significant figures.

Answer 1

167,886,383 basketballs

Explanation:

We are asked to find how many basketballs would take to circle around the equator. We have given the earth's radius. So, we need the formula to obtain it's perimeter. Thus:

`Perimeter = Pi*diameter [m]\\Where Pi = 3.14`

Earth's diameter is simply radius*2. It means:

`P= 3.14*6400*2 = 40,192 [km]`

On the other hand, we have a basketball crcumference; however, we need to obtain its diameter so that we can later calculate how many basketballs fit on earth's equator by simply dividing earth's circumference by a basketball's diameter.

Diameter of a basketball:

`D= Perimeter /Pi [m]`

We need to change units to fit in the international system.

29.6 in to cm =
`29.6*2.54 = 75.184 [cm]`

Then:

`Diameter=75.184/3.14 = 23.94 [cm]`

We have to convert earth's perimeter in km to cm:

`Equator=40192[km]*100000=4,019,200,000 [cm]`

Finally, dividing total earth's circumference by a basketball diameter:

`Totalbasketballs=4,019,200,000/23.94= 167,886,383 [basketballs]`