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.

Question

asked Apr 10, 2019 17.5k views

1 Answer

Phil Rykoff · Answer 1 · 2019-04-14T19:13:13+0000

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
is the radius (
r=(16cm)/(2)=8cm ) and
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:

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