Question

12 spheres of the same size are made from melting a solid cylinder of 1 cm diameter and 2 cm height. Find the diameter of each sphere.

Answer 1

The answer is: The diameter is 4 centimeters.

The explanation is shown below:

1. The volume of the cylinder is:

`Vc=r^(2)h \pi`

Where
`r` is the radius (
`r=(16cm)/(2)=8cm`) and
`h` is the height (
`h=2cm`).

Then:

`Vc=(8cm)^(2)}(2cm)\pi\\Vc=128\pi`

2. The total volume of the 12 spheres is:

`Vs=12((4)/(3)r^(3)\pi)\\Vs=16r^(3)\pi`

3. The volume of the cylinder and the total volume of all the 12 spheres, are equal, therefore:

`Vc=Vs\\128\pi=16r^(3)\pi`

4. Now, you must solve for the radius:

`r=\sqrt[3]{(128\pi)/(16\pi)}\\r=2cm`

5. The diameter is:

`d=2r\\d=2(2cm)\\d=4cm`