To find the radius of a sphere given its volume, we will use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( V \)[/tex] is the volume and [tex]\( r \)[/tex] is the radius. We are given that the volume [tex]\( V \)[/tex] is 34 cm³.
Step-by-Step Solution:
1. Substitute the given volume into the formula:
[tex]\[ 34 = \frac{4}{3} \pi r^3 \][/tex]
2. Rearrange the formula to solve for [tex]\( r^3 \)[/tex] by isolating [tex]\( r^3 \)[/tex]:
[tex]\[ \frac{4}{3} \pi r^3 = 34 \][/tex]
3. Multiply both sides by the reciprocal of [tex]\( \frac{4}{3} \pi \)[/tex]:
[tex]\[ r^3 = \frac{34 \cdot 3}{4 \cdot \pi} \][/tex]
4. Calculate the numerical value:
[tex]\[ r^3 = \frac{102}{4 \pi} \][/tex]
Using [tex]\( \pi \approx 3.14159 \)[/tex]:
[tex]\[ r^3 \approx \frac{102}{4 \times 3.14159} \][/tex]
[tex]\[ r^3 \approx \frac{102}{12.56636} \][/tex]
[tex]\[ r^3 \approx 8.118 \][/tex]
5. To find [tex]\( r \)[/tex], take the cube root of both sides:
[tex]\[ r \approx \sqrt[3]{8.118} \][/tex]
Calculate the cube root:
[tex]\[ r \approx 2 \][/tex]
Thus, the approximate radius of a sphere with a volume of 34 cm³ is 2 cm.
So, the correct answer is:
B. 2 cm
