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.

The answer is: The diameter is 4 centimeters.

The explanation  is shown below:

1. The volume of the cylinder is:

Where is the radius () and is the height ().

Then:

2. The total volume of the 12 spheres is:

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

4. Now, you must solve for the radius:

5. The diameter is:

no this is a nonlinear negative

the given 6 = w/p is equivalent to 6p = w, where w is the total area of the walls and p is the area covered by a single can of paint.

knowing that 6 cans of paint will be needed, 6p = w becomes 6(6) = w = 36.   this tells us that the total area to be painted is 36 square units.