Determine the volume of the sphere.

Question

A sphere just fits inside a cube with edges 18cm long

a) determine the volume of the sphere

b) determine the volume of the cube

c) how much empty space is inside the cube unoccupied by the sphere?

I don't understand this question because i feel like I'm only given one piece of information. what am i supposed to do with the 18cm?? please help

Answer 1

You are given one piece of information and you only need that one.

Volume of a cube = length * length * length

Volume of a sphere = 4/3 * π * r^3

Now the fattest part of the sphere is at the equator; any fatter and the sphere won't drop into the cube

That's the diameter

Can you see that the length of the cube and the diameter of the sphere is that one piece of information?

Use it to calculate the two different volumes

The difference is the unoccupied space in the cube