Question

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

Explanation:

Step1: Recall the volume formula for a sphere

The volume formula for a sphere is \(V = \frac{4}{3}\pi r^{3}\).

Step2: Calculate the volume of the small sphere

Let the radius of the small sphere \(r_{1}=3\). Then \(V_{1}=\frac{4}{3}\pi(3)^{3}=\frac{4}{3}\pi\times27 = 36\pi\).

Step3: Calculate the volume of the large sphere

Let the radius of the large sphere \(r_{2} = 6\). Then \(V_{2}=\frac{4}{3}\pi(6)^{3}=\frac{4}{3}\pi\times216=288\pi\).

Step4: Find the ratio of the volumes

\(\frac{V_{2}}{V_{1}}=\frac{288\pi}{36\pi}\). Since \(\pi\) cancels out, \(\frac{288}{36}=8\).

Answer:

8