Answer:
12 cm^3
Step-by-step explanation:
Before we do anything, we should set up the proportion.
[tex]\frac{\pi * r^2*h}{\frac{4\pi r^3}{3}} = \frac{18}{x}[/tex]
Now do the Cancelations of \pi r^2 on the left.
h// (4/3) r = 18/x
but h = 2*r
2r // (4/3) * r = 18/x Cancel the rs on the left
2// (4/3) = 18/x Make 2 = 2/1 so you can handle the fraction
2/1 // (4/3) = 18/x Invert and multiply the denominator
2/1 * 3/4 = 18/x
6/4 = 18x You can reduce the left side
3/2 = 18x Cross multiply
3x = 2*18 Combine the right
3x = 36 Divide by 3
x = 12
So what you have found is the volume of the sphere. 12 cm^3
This is a very interesting question. Keep in mind that physics does this all the time for any of the force formulas (but not all).
I'm a little long winded here, but the first time you see this, you should be given very small steps.
