5 Find the radius of a spherical ball bearing that has a volume of $$ 7.24 \mathrm{~cm}^{3} $$.

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UpStudy AI · Accepted Answer

**Step 1. Write the formula for the volume of a sphere**  
The volume $$ V $$ of a sphere with radius $$ r $$ is given by  
$$
V = \frac{4}{3} \pi r^3.
$$

**Step 2. Substitute the known volume and solve for $$ r $$**  
Given $$ V = 7.24 \, \text{cm}^3 $$, we have  
$$
\frac{4}{3} \pi r^3 = 7.24.
$$  
To solve for $$ r^3 $$, multiply both sides by $$ \frac{3}{4\pi} $$:  
$$
r^3 = \frac{7.24 \times 3}{4\pi}.
$$

**Step 3. Evaluate the numerical expression**  
First, calculate the numerator:  
$$
7.24 \times 3 = 21.72.
$$  
Then, the expression becomes  
$$
r^3 = \frac{21.72}{4\pi}.
$$  
Approximating $$ \pi \approx 3.14159 $$, compute the denominator:  
$$
4\pi \approx 4 \times 3.14159 = 12.56636.
$$  
Thus,  
$$
r^3 \approx \frac{21.72}{12.56636} \approx 1.729.
$$

**Step 4. Extract the cube root to find $$ r $$**  
Taking the cube root of both sides gives  
$$
r \approx \sqrt[3]{1.729}.
$$  
Since $$ 1.2^3 = 1.728 $$, it follows that  
$$
r \approx 1.2 \, \text{cm}.
$$

**Final Answer:**  
The radius of the spherical ball bearing is approximately $$ 1.2 \, \text{cm} $$.
The radius of the spherical ball bearing is approximately $$ 1.2 \, \text{cm} $$.

5 Find the radius of a spherical ball bearing that has a volume of .

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