Question

the volume of a soap bubble is 659.2 mm³. find the radius and diameter of the soap bubble. use 3.14 for π.
the radius of the bubble is about mm.
(round to the nearest tenth as needed.)

Explanation:

Step1: Recall volume formula for sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where $V$ is the volume and $r$ is the radius. We know $V = 659.2\ mm^{3}$ and $\pi=3.14$.

Step2: Solve for radius $r$

First, substitute the values into the formula: $659.2=\frac{4}{3}\times3.14\times r^{3}$.
Then, simplify the right - hand side: $\frac{4}{3}\times3.14 = 4.1866\cdots$. So the equation becomes $659.2 = 4.1866\cdots r^{3}$.
Next, solve for $r^{3}$: $r^{3}=\frac{659.2}{4.1866\cdots}=157.45$.
Finally, find $r$: $r=\sqrt[3]{157.45}\approx5.4\ mm$.

Step3: Calculate the diameter $d$

The diameter $d = 2r$. So $d=2\times5.4 = 10.8\ mm$.

Answer:

The radius of the bubble is about $5.4\ mm$.
The diameter of the bubble is about $10.8\ mm$.