\[ \frac{4}{3}r^3 = 288 \]

["Solving (\frac{4}{3}r^3 = 288): A Step-by-Step Guide", "If you've ever come across the equation (\frac{4}{3}r^3 = 288), solving for (r) is straightforward once you understand the algebra involved. This equation arises in various real-world applications—such as geometry and volume calculations—making it a valuable problem to master.", "In this SEO-optimized guide, we’ll walk you through solving (\frac{4}{3}r^3 = 288) step-by-step, using clear explanations and targeted keywords to boost visibility for students, math enthusiasts, and educators searching for help with solving cubic equations.", "---", "### What Is (\frac{4}{3}r^3 = 288)?", "The equation (\frac{4}{3}r^3 = 288) defines a cube-shaped relationship. Here, (r^3) represents the cube of an unknown variable (r), scaled by (\frac{4}{3}), equaling 288. Solving for (r) gives the linear dimension tied to a volume or geometric shape defined by this cubic term.", "---", "### Step-by-Step Solution: How to Solve (\frac{4}{3}r^3 = 288)", "#### Step 1: Eliminate the fraction\nMultiply both sides by 3 to eliminate the denominator:", "[\n3 \cdot \left( \frac{4}{3}r^3 \right) = 3 \cdot 288\n\quad\Rightarrow\quad\quad\quad\quad 4r^3 = 864\n]", "#### Step 2: Isolate (r^3)\nDivide both sides by 4:", "[\nr^3 = \frac{864}{4} = 216\n]", "#### Step 3: Take the cube root\nTo solve for (r), take the cube root of both sides:", "[\nr = \sqrt[3]{216} = 6\n]", "---", "### Why This Equation Matters", "Solving cubic equations like (\frac{4}{3}r^3 = 288) is essential in:", "- Geometry: When calculating the edge length of a cube given its volume as (\frac{4}{3}r^3).\n- Physics: Found in formulas involving scale and dimensional analysis.\n- Engineering & Design: Used to determine dimensions where cubic growth or container volumes are involved.", "---", "### Final Answer", "[\nr = 6\n]", "---", "### Tips for Solving Similar Equations", "- Always clear fractions early to simplify calculations.\n- Isolate the cubic term.\n- Use inverse operations: cube root after scaling.\n- Check your answer by plugging (r = 6) back into the original equation.", "---", "Keywords: solve (\frac{4}{3}r^3 = 288), cubic equation solution, algebra tips, how to solve (r^3 = 216), geometry using algebra, cube root tutorial, step-by-step equation solving.", "---", "Conclusion\nSolving (\frac{4}{3}r^3 = 288) is a fundamental algebraic skill with broad applications. By following the clear, step-by-step process above, anyone—from students to professionals—can master cubic equations and tackle complex mathematical problems with confidence.", "For more math tutorials and algebraic tricks, visit us for comprehensive guidance!", "---", "Meta Description: Step-by-step solution to solve (\frac{4}{3}r^3 = 288), including algebra tips, cube root explanation, and real-world applications for students and educators."]