Divide both sides by \(\pi\): \( 4r^2 = 144 \).

["# Dividing Both Sides by (\pi): Solving ( 4r^2 = 144 )", "When working with equations involving variables and constants like (\pi), one of the foundational steps algebra teaches is dividing both sides by a common factor to isolate the variable. In this article, we’ll explore how dividing both sides of the equation ( 4r^2 = 144 ) by (\pi) (or more precisely, simplifying appropriately) helps solve for ( r ), and why this process matters in mathematical problem-solving.", "## Understanding the Equation\nThe given equation is:\n[\n4r^2 = 144\n]\nHere, ( r ) is the variable representing radius—commonly appearing in formulas related to circles, cylinders, and spheres. Though (\pi) does not explicitly appear in this particular equation, understanding how to handle (\pi) is crucial in geometry, especially in formulas involving area (( \pi r^2 )), circumference, or volume.", "While (\pi) is absent, dividing both sides by a constant is a powerful technique applicable when coefficients appear with variables. This principle extends naturally when equations involve (\pi), particularly in equations like:\n[\n\pi r^2 = 144\n]\nHere, dividing both sides by (\pi) clearly isolates ( r^2 ), demonstrating the core strategy we’ll apply.", "## Dividing Both Sides by a Constant\nThe method of dividing both sides of an equation by a constant is rooted in the multiplicative inverse property—if ( a = b ), then ( \frac{a}{c} = \frac{b}{c} ) for any ( c <br/>\neq 0 ). This preserves equality while simplifying expressions.", "Step-by-step process for ( 4r^2 = 144 ):\n1. Start with the equation:\n[\n4r^2 = 144\n]\n2. To isolate ( r^2 ), divide both sides by 4:\n[\n\frac{4r^2}{4} = \frac{144}{4}\n]\n3. Simplify:\n[\nr^2 = 36\n]\n4. To solve for ( r ), take the square root of both sides:\n[\nr = \pm 6\n]\nHowever, in most geometric contexts like radius values, only the positive root is physically meaningful.", "## Why This Matters—Applying to (\pi)-Based Formulas\nImagine applying this to a real-world scenario:\nSuppose ( 4r^2 = 144\pi ). Dividing both sides by 4 yields:\n[\nr^2 = 36\pi\n]\nTaking the square root gives:\n[\nr = \sqrt{36\pi} = 6\sqrt{\pi}\n]\nThis illustrates how constants like (\pi) weave into algebraic manipulation, especially in geometry. Understanding to divide properly allows you to isolate variables even when constants involve transcendental numbers like (\pi).", "## Final Answer\nFor the original equation ( 4r^2 = 144 ), dividing both sides by 4 gives:\n[\nr^2 = 36\n]\nThus,\n[\nr = \pm 6\n]\n(Only ( r = 6 ) is valid if radius is non-negative.)", "## Key Takeaways\n- Dividing both sides of an equation by a constant maintains equality and simplifies isolation of variables.\n- This method applies even when係数 like (\pi) appear implicitly—just divide directly by the known constant.\n- Solving ( r^2 = 36 ) yields ( r = \pm 6 ), but context determines viable solutions.\n- Mastering this step strengthens foundational algebra skills essential for more complex problems involving (\pi) in trigonometry, geometry, and calculus.", "If you're studying equations with (\pi), remember: divide strategically, simplify carefully, and always interpret solutions within real-world constraints.", "---\nKeywords: divide both sides by (\pi), solve for ( r ), geometric equations, algebra basics, radius calculation, simplify equations."]