So with this equation, since the volume of the cylinder is 96 pi, plug that into the V variable, and since the radius of one of the marbles is 3, plug that into the r variable. From here, we can solve for x: [tex] 96\pi =24\pi +x(\frac{4}{3}\pi*3^3) [/tex]
Firstly, solve the parentheses: [tex] 96\pi =24\pi +x(\frac{4}{3}\pi*27)\\ 96\pi =24\pi +x(36\pi) [/tex]
Next, multiply 36 pi and x: [tex] 96\pi = 24\pi +36\pi x [/tex]
Next, subtract 24 pi on both sides: [tex] 72\pi =36\pi x [/tex]
Lastly, divide both sides by 36 pi, and your answer will be [tex] 2=x [/tex], or B.
