Question

I’m studying for my Sat later in the month, and even using the answer key I don’t understand how to solve this question. Help?

Answer 1

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: $96\pi =24\pi +x(\frac{4}{3}\pi*3^3)$

Firstly, solve the parentheses: $96\pi =24\pi +x(\frac{4}{3}\pi*27)\\ 96\pi =24\pi +x(36\pi)$

Next, multiply 36 pi and x: $96\pi = 24\pi +36\pi x$

Next, subtract 24 pi on both sides: $72\pi =36\pi x$

Lastly, divide both sides by 36 pi, and your answer will be $2=x$, or B.