Answer:
VA/VB = 8
Step-by-step explanation:
You have a sphere A with diameter 12, that is, radius 6, which can be written as follow:
[tex]V_A=\frac{4}{3}\pi r_A^3=\frac{4}{3}\pi (6)^3=288\pi[/tex] (1)
The sphere A is dilated by a scale factor of one half to sphere B. Then, you have:
[tex]V_B=\frac{4}{3}\pi r_B^3=\frac{4}{3}\pi (\frac{6}{2})^3=36\pi[/tex] (2)
From the results of equation (2) and (1) you can calculate the ratio VA/VB:
[tex]\frac{V_A}{V_B}=\frac{288\pi}{36\pi}=8[/tex]
The ratio of the volumes of both sphere A and B is 8
