If the radius of a circle is increased by 50%, what happens to the area of the c

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Question: If the radius of a circle is increased by 50%, what happens to the area of the circle?

Options:

Correct Answer: It increases by 125%.

Solution:

If the radius increases by 50%, the new radius is 1.5r, and the area becomes (1.5r)² = 2.25r², which is a 125% increase.

If the radius of a circle is increased by 50%, what happens to the area of the circle?

If the radius of a circle is increased by 50%, what happens to the area of the circle?

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 '1.5r'.
Step 3: The formula for the area of a circle is A = πr².
Step 4: Substitute the new radius into the area formula: A = π(1.5r)².
Step 5: Calculate (1.5r)², which equals 2.25r².
Step 6: So, the new area is A = π(2.25r²) = 2.25πr².
Step 7: Compare the new area (2.25πr²) to the original area (πr²).
Step 8: The increase in area is 2.25πr² - πr² = 1.25πr².
Step 9: This means the area has increased by 1.25 times the original area, which is a 125% increase.

Circle Area Calculation – Understanding how to calculate the area of a circle using the formula A = πr² and how changes in the radius affect the area.
Percentage Increase – Calculating the percentage increase in area when the radius is increased by a certain percentage.