the radius of the large sphere is double the radius of the small sphere. how many times is the volume of the…

Explanation:

Step1: Recall volume formula for sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$.

Step2: Calculate volume of small sphere

Let the radius of the small sphere $r_1 = 3$. Then $V_1=\frac{4}{3}\pi r_1^{3}=\frac{4}{3}\pi\times3^{3}= 36\pi$.

Step3: Calculate volume of large sphere

The radius of the large sphere $r_2 = 6$. Then $V_2=\frac{4}{3}\pi r_2^{3}=\frac{4}{3}\pi\times6^{3}=288\pi$.

Step4: Find the ratio of volumes

$\frac{V_2}{V_1}=\frac{288\pi}{36\pi}=8$.

Answer:

8