Question

question 7 (multiple choice worth 1 points) (06 02 mc) sphere a has a diameter of 2 and is dilated by a scale factor of 3 to create sphere b. what is the ratio of the volume of sphere a to sphere b? o 1/27 o 1/9 o 4/36 o 2/6

Explanation:

Step1: Recall volume formula for sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. For sphere A, the diameter $d_A=2$, so the radius $r_A = 1$. For sphere B, since it is dilated from sphere A by a scale - factor of 3, the radius $r_B=3r_A = 3$.

Step2: Calculate volumes of sphere A and B

The volume of sphere A, $V_A=\frac{4}{3}\pi r_A^{3}=\frac{4}{3}\pi(1)^{3}=\frac{4}{3}\pi$. The volume of sphere B, $V_B=\frac{4}{3}\pi r_B^{3}=\frac{4}{3}\pi(3)^{3}=36\pi$.

Step3: Find the ratio of volumes

The ratio of the volume of sphere A to sphere B is $\frac{V_A}{V_B}=\frac{\frac{4}{3}\pi}{36\pi}=\frac{4}{3}\times\frac{1}{36}=\frac{1}{27}$.

Answer:

1/27