If the radius of a circle is increased by 50%, by what percentage does the area
Practice Questions
Q1
If the radius of a circle is increased by 50%, by what percentage does the area of the circle increase?
25%
50%
75%
100%
Questions & Step-by-Step Solutions
If the radius of a circle is increased by 50%, by what percentage does the area of the circle increase?
Step 1: Understand that the area of a circle is calculated using the formula A = πr², where r is the radius.
Step 2: Note that if the radius is increased by 50%, the new radius becomes 1.5 times the original radius (r). So, new radius = 1.5r.
Step 3: Calculate the new area using the new radius. Substitute 1.5r into the area formula: A' = π(1.5r)².
Step 4: Simplify the new area calculation: A' = π(1.5r)² = π(2.25r²) = 2.25πr².
Step 5: Compare the new area (A') with the original area (A). The original area is A = πr².
Step 6: To find the increase in area, calculate the difference: Increase = A' - A = 2.25πr² - πr² = (2.25 - 1)πr² = 1.25πr².
Step 7: To find the percentage increase, divide the increase by the original area and multiply by 100: Percentage Increase = (1.25πr² / πr²) * 100 = 125%.
Step 8: Conclude that the area of the circle increases by 125% when the radius is increased by 50%.
