\[ 150 = \frac{25\pi}{3} h \]

["Solving 150 = (25π/3)h: Step-by-Step Explanation", "Understanding how to solve equations like ( 150 = \frac{25\pi}{3} h ) is essential in many mathematical and real-world applications, from physics to engineering. This article breaks down the step-by-step solution for ( h ) and explains the concept clearly.", "---", "### What is the Equation?", "We begin with the equation:", "[\n150 = \frac{25\pi}{3} h\n]", "Our goal is to isolate ( h ), the unknown variable, and solve for it.", "---", "### Step 1: Isolate ( h )", "To solve for ( h ), divide both sides of the equation by ( \frac{25\pi}{3} ). Alternatively, you can multiply both sides by the reciprocal:", "[\nh = 150 \div \left( \frac{25\pi}{3} \right)\n]", "Dividing by a fraction is the same as multiplying by its reciprocal, so:", "[\nh = 150 \ imes \frac{3}{25\pi}\n]", "---", "### Step 2: Simplify the Expression", "Now simplify the left-hand side:", "[\nh = \frac{150 \ imes 3}{25\pi} = \frac{450}{25\pi}\n]", "Reduce the fraction by dividing numerator and denominator by 25:", "[\nh = \frac{18}{\pi}\n]", "---", "### Final Result", "[\nh = \frac{18}{\pi}\n]", "This exact value can be approximated numerically using ( \pi \approx 3.1416 ):\n[\nh \approx \frac{18}{3.1416} \approx 5.73\n]", "---", "### Practical Insight", "The solution ( h = \frac{18}{\pi} ) expresses the height ( h ) in terms of the constant ( \pi ) and the numerical factor ( 150 ). This form reveals a proportional relationship between height and the given constants, useful in modeling circular or curved systems where ( \pi ) naturally appears.", "---", "### Multiple Choice & Verification (Bonus Section)", "Guessing the simplified form of ( h ) is common. Among possible approximations:", "- Option A: ( h = 5.7 ) — close but not exact\n- Option B: ( h = \frac{18}{\pi} ) — correct exact value\n- Option C: ( h = 6\pi ) — incorrect, units mismatch", "✅ Correct Answer: ( h = \frac{18}{\pi} )", "---", "### Conclusion", "Solving ( 150 = \frac{25\pi}{3} h ) involves basic algebra: isolate ( h ) via division and simplify the fraction. The elegant exact answer ( h = \frac{18}{\pi} ) showcases how rational and transcendental numbers work together in mathematical modeling. Whether calculating dimensions, frequencies, or rates involving circular geometry, mastering such equations strengthens problem-solving skills across science and engineering.", "---", "Keywords: solve equation 150 = (25π/3)h, mathematical solution, isolate h, exact value, π approximation, algebra steps, solve for h, frequency, circular motion formula.\nMeta Description: Solve the equation 150 = (25π/3)h step-by-step to find h = 18/π. Learn how to isolate variables and simplify with π.\nRelated Terms: algebraic equations, solving for height, circular geometry applications, mathematics tutorial."]