1. The problem asks to find the radius $r$ of a sphere given its volume $V = 904.8$ cm$^3$ using the formula: $$r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}$$ where $\pi \approx 3.14$. 2. Substitute the given volume into the formula: $$r = \left(\frac{3 \times 904.8}{4 \times 3.14}\right)^{\frac{1}{3}}$$ 3. Calculate the numerator and denominator inside the parentheses: $$3 \times 904.8 = 2714.4$$ $$4 \times 3.14 = 12.56$$ So, $$r = \left(\frac{2714.4}{12.56}\right)^{\frac{1}{3}}$$ 4. Divide inside the parentheses: $$\frac{2714.4}{12.56} \approx 216.07$$ 5. Now find the cube root of 216.07: Since $6^3 = 216$, the cube root of 216.07 is approximately 6. 6. Therefore, the radius $r$ is approximately 6 cm. Final answer: $r \approx 6$ cm.