Answer:
[tex]768\pi = 1024\pi - 16\pi r^2[/tex]
[tex]r = 4[/tex]
Step-by-step explanation:
See attachment for complete question
Given
[tex]v = 1.024\pi - 16\pi r^2[/tex]
Required
Determine the equation and solution when v = 768
[tex]v = 1024\pi - 16\pi r^2[/tex]
Substitute [tex]768\pi[/tex] for v
[tex]768\pi = 1024\pi - 16\pi r^2[/tex]
The above expression represents the equation
Solving further:
[tex]768\pi = 1024\pi - 16\pi r^2[/tex]
Collect like terms
[tex]16\pi r^2 = 1024\pi - 768\pi[/tex]
[tex]16\pi r^2 = 256\pi[/tex]
Divide both sides by [tex]16\pi[/tex]
[tex]r^2 = \frac{256\pi}{16\pi}[/tex]
[tex]r^2 = \frac{256}{16}[/tex]
[tex]r^2 = 16[/tex]
Take square roots of both sides
[tex]r = \sqrt{16[/tex]
[tex]r = 4[/tex]
