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

₹0.0

Question: In a circle, if the radius 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. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.

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

In a circle, if the radius 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: Let the original radius be 'r'.
Step 3: If the radius is increased by 50%, the new radius becomes 1.5 times the original radius, which is 1.5r.
Step 4: The formula for the area of a circle is A = πr².
Step 5: Substitute the new radius (1.5r) into the area formula: A = π(1.5r)².
Step 6: Calculate (1.5r)², which is 2.25r².
Step 7: Now, the area becomes A = π(2.25r²) = 2.25πr².
Step 8: Compare the new area (2.25πr²) to the original area (πr²).
Step 9: The new area is 2.25 times the original area, which means it has increased by 125%.

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.