Question

A manufacturer makes two different sizes of spherical ball bearings for use in motors. If the radius of the larger ball bearing is twice the radius of the smaller one, then the volume of the larger ball bearing is how many times the volume of the smaller one?

Answer 1

The volume of the larger ball bearing is 8 times the volume of the

smaller one

Step-by-step explanation:

All the spheres are similar, and there is a ratio between their radii $\frac{r_{1}}{r_{2}}$

So the ratio between their:

1. Diameters⇒ $\frac{d_{1}}{d_{2}}$ = $\frac{r_{1}}{r_{2}}$

2. Areas ⇒ $\frac{A_{1}}{A_{2}}$ = $(\frac{r_{1}}{r_{2}})^{2}$

3. Volumes ⇒ $\frac{V_{1}}{V_{2}}$ = $(\frac{r_{1}}{r_{2}})^{3}$

∵ The radius of the larger ball bearing is twice the radius of the

   smaller one

-  That means the radius of the larger sphere is equal to the radius

    of the smaller sphere multiplied by 2

∴ $\frac{r_{1}}{r_{2}}$ = $\frac{2}{1}$

∵ $\frac{V_{1}}{V_{2}}$ = $(\frac{r_{1}}{r_{2}})^{3}$

∴ $\frac{V_{1}}{V_{2}}$ = $(\frac{2}{1})^{3}$

∴ $\frac{V_{1}}{V_{2}}$ = $\frac{8}{1}$

The volume of the larger ball bearing is 8 times the volume of the

smaller one

Learn more:

You can learn more about ratios in brainly.com/question/4302397

brainly.com/question/4713715

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