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 ($r=\frac{16cm}{2}=8cm$) 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:

$Vs=12(\frac{4}{3}r^{3}\pi)\\Vs=16r^{3}\pi$

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:

$r=\sqrt[3]{\frac{128\pi}{16\pi}}\\r=2cm$

5. The diameter is:

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