Question

the radius of the large sphere is double the radius of the small sphere. how many times is the volume of the large sphere than the small sphere? 2 4 6 8

Explanation:

Step1: Recall the formula for the volume of a sphere

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\), where \(r\) is the radius of the sphere.

Step2: Calculate the volume of the small sphere

For the small sphere with \(r = 3\), \(V_{s}=\frac{4}{3}\pi(3)^{3}=\frac{4}{3}\pi\times27 = 36\pi\).

Step3: Calculate the volume of the large sphere

For the large sphere with \(r = 6\), \(V_{l}=\frac{4}{3}\pi(6)^{3}=\frac{4}{3}\pi\times216=288\pi\).

Step4: Find the ratio of the volumes

\(\frac{V_{l}}{V_{s}}=\frac{288\pi}{36\pi}\). Since \(\pi\) cancels out (\(\pi
eq0\)), \(\frac{288}{36}=8\).

Answer:

8