In a circle, if the radius is increased by 50%, what happens to the area?

In a circle, if the radius is increased by 50%, what happens to the area?

Step 1: Understand that the radius of a circle is the distance from the center to the edge.
Step 2: If the original radius is 'r', increasing it by 50% means the new radius is 1.5 times the original radius. So, new radius = 1.5r.
Step 3: The formula for the area of a circle is A = πr². We will use this formula to find the area with the new radius.
Step 4: Substitute the new radius (1.5r) into the area formula: A = π(1.5r)².
Step 5: Calculate (1.5r)², which is (1.5)² * r² = 2.25 * r².
Step 6: Now, substitute this back into the area formula: A = π * 2.25 * r² = 2.25πr².
Step 7: Compare the new area (2.25πr²) to the original area (πr²). The original area is πr².
Step 8: To find the increase in area, subtract the original area from the new area: 2.25πr² - πr² = 1.25πr².
Step 9: To find the percentage increase, divide the increase (1.25πr²) by the original area (πr²): (1.25πr²) / (πr²) = 1.25.
Step 10: Convert this to a percentage: 1.25 = 125%. This means the area increases by 125%.

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