To find the radius of a sphere given its volume, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius. We are given that the volume \( V \) is 34 cm³, so we can set up the equation:
\[ 34 = \frac{4}{3} \pi r^3 \]
To solve for \( r \), first multiply both sides by \( \frac{3}{4} \):
\[ r^3 = \frac{34 \times 3}{4 \pi} \]
Calculating that step by step:
- Calculate \( 34 \times 3 = 102 \)
- Then, \( \frac{102}{4} = 25.5 \)
- Now divide by \( \pi \): \( \frac{25.5}{\pi} \approx \frac{25.5}{3.14} \approx 8.13 \)
Now, we need to take the cube root to find \( r \):
\[ r \approx \sqrt[3]{8.13} \approx 2.0 , \text{cm} \]
Thus, the approximate radius of the sphere is:
B. 2 cm