A circle has a radius of 8 units. If the radius is increased by 50%, what is the new area of the circle?
["How to Calculate the Area of a Circle After Increasing the Radius – A Practical Example with a Radius of 8 Units", "When studying geometry, one of the most essential concepts is understanding the area of a circle. The area ( A ) of a circle is calculated using the formula:", "[ A = \pi r^2 ]", "where ( r ) is the radius. In this article, we’ll explore a common scenario: what happens to the area when the radius is increased by 50%. Let’s take a circle with a radius of 8 units and increase it by 50% to uncover the new area.", "### Starting Point: Original Radius", "Given:\n- Original radius ( r = 8 ) units", "Original area calculation:\n[\nA = \pi (8)^2 = \pi \ imes 64 = 64\pi\n]", "This means the original area is ( 64\pi ) square units.", "### Step 1: Increase the Radius by 50%", "To increase 8 units by 50%:\n[\n\ ext{Increase} = 8 \ imes 0.50 = 4\n]\n[\n\ ext{New radius} = 8 + 4 = 12 \ ext{ units}\n]", "### Step 2: Calculate the New Area", "Using the area formula with the new radius of 12:\n[\nA_{\ ext{new}} = \pi (12)^2 = \pi \ imes 144 = 144\pi\n]", "So, the new area is ( 144\pi ) square units.", "### Why This Matters: Understanding Area Changes", "Increasing the radius by 50% doesn’t just change the size uniformly — it dramatically increases the area. In this case, the radius grew by half, but the area quadrupled (from ( 64\pi ) to ( 144\pi )). This demonstrates the quadratic relationship between radius and area.", "---", "Summary\n- Original radius: 8 units\n- Increased radius: 12 units\n- Original area: ( 64\pi ) square units\n- New area after 50% increase: ( 144\pi ) square units", "For students and math enthusiasts, understanding how changing the radius impacts area helps grasp key geometric principles applicable in real-world problems — from architecture to engineering.", "Keywords: circle area formula, radius increase, how to calculate area, geometry basics, increase radius by 50%, formula application.\nMeta Description: Learn how to calculate the new area of a circle when the radius increases by 50%, using a radius of 8 units as an example.", "---", "Bonus Tip: Remember: area grows with the square of the radius. A 50% increase in radius leads to a 125% increase in area (((12/8)^2 = 2.25)) — a vital insight in mathematical problem-solving."]
