Final answer:
When the radius of a circle is halved, the area becomes one-quarter of the original area. This is shown by substituting ½ r into the area formula A = πr², which gives the new area as ¼ of the original area.
Step-by-step explanation:
The question revolves around understanding how the area of a circle changes when its radius is halved. The area of a circle is given by the formula A = πr², where A is the area and r is the radius. To find the effect of reducing the radius by half, we can substitute ½ r for r in the equation.
Let's calculate the new area:
A' = π(½ r)² = π(¼ r²) = ¼ πr²
This shows that the new area, A', is one-quarter (¼) of the original area. Thus, if the radius of a circle is cut down to half, the area of the circle becomes one-quarter of what it was originally.
Example:
If the original area of the circle was 16π when the radius is halved, the new area would be:
A' = 1/4 × 16π = 4π
As seen in the example, the reduced radius has a significant impact, decreasing the area of the circle significantly.