Solve the following problem using the formula $V=\frac{4}{3} \pi r^{3}$ where $V$, the volume of a sphere, depends on $r$, its radius in centimeters.
Determine the radius (in centimeters) if the volume is $3,979,948$ cubic centimeters.
Round to two decimal places.
Answer
Final Answer: The radius of the sphere is approximately \(\boxed{98.31}\) centimeters.
Step 1 ：We are given the volume of the sphere and we need to find the radius. We can rearrange the formula to solve for the radius. The rearranged formula would be \(r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}\).
Step 2 ：We can then substitute the given volume into the formula and solve for the radius.
Step 3 ：Substituting the given volume, \(V = 3979948\), into the formula, we get \(r = \left(\frac{3 \times 3979948}{4\pi}\right)^{\frac{1}{3}}\).
Step 4 ：Solving for \(r\), we get \(r = 98.30967555823234\).
Step 5 ：Rounding to two decimal places, we get \(r = 98.31\).
Step 6 ：Final Answer: The radius of the sphere is approximately \(\boxed{98.31}\) centimeters.
