Question

r = 2 mm volume of sphere = \\(\frac{4}{3}\pi r^3\\) \\(\pi \approx 3.14\\) what is the approximate volume of the marble? \\(\bigcirc\\) a. \\(16.7\\,\text{mm}^3\\) \\(\bigcirc\\) b. \\(25.0\\,\text{mm}^3\\) \\(\bigcirc\\) c. \\(32.0\\,\text{mm}^3\\) \\(\bigcirc\\) d. \\(33.5\\,\text{mm}^3\\) \\(\bigcirc\\) e. \\(100.5\\,\text{mm}^3\\)

Explanation:

Step1: Identify the formula and given values

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \), and the radius \( r = 2\space mm \), \( \pi\approx3.14 \).

Step2: Substitute the values into the formula

First, calculate \( r^{3} \): \( r^{3}=2^{3}=8 \).
Then, substitute \( r^{3}=8 \) and \( \pi\approx3.14 \) into the formula:
\( V=\frac{4}{3}\times3.14\times8 \)

Step3: Perform the calculation

First, calculate \( \frac{4}{3}\times8=\frac{32}{3}\approx10.67 \).
Then, multiply by \( 3.14 \): \( 10.67\times3.14\approx33.5 \space mm^{3} \).

Answer:

D. \( 33.5\space mm^{3} \)