Problem

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.

Solution

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.

From Solvely APP
Source: https://solvelyapp.com/problems/20078/

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