Question

Three tennis balls are packed tightly in a rectangular box.

What is the ratio of the volume of the tennis balls to the volume of the box?

Answer 1

It's not 100% clear, but I'm assuming the tennis balls are packed like this

Answer 2

it's not drawn perfectly since the 3 tennis balls are supposed to touch

Answer 3

anyways, let's say the diameter of one ball is 1 unit



what would be the length of the rectangle?

Answer 4

Yes thats what it looks like. The length of the rectangle would be 3

Answer 5

good

Answer 6

what is the width of the rectangle?

Answer 7

1

Answer 8

correct

Answer 9

what is the height of the box?

Answer 10

Isn't the height the same as the length? so 3?

Answer 11

not quite

Answer 12

imagine we have this 3D box

Answer 13

we found the length and width so far

Answer 14

the height is the same as the diameter of each ball (to make sure they fit in terms of the height), so the height is 1

Answer 15

Okay, that makes sense

Answer 16

what is the volume of that rectangular box?

Answer 17

The volume is 3

Answer 18

3 cubic units, good

Answer 19

if a sphere has a diameter of 1, what is the volume of that sphere?

Answer 20

4.2 cubic units?

Answer 21

If you used the formula

V = (4/3)*pi*r^3

then you are correct

Answer 22

but remember the diameter is 1, so the radius would be half that: 1/2 = 0.5

Answer 23

so you should have

V = (4/3)*pi*(0.5)^3

V = ??

Answer 24

Oh yeah thats right, so the volume is actually .524. But since there is three of them we times it by 3?

Answer 25

I'm getting 0.5235987755983, so it looks like you got it