Question 3

The area of the circle is increased by 800% when the radius is tripled.

When the radius of a circle is tripled, the area increases by 800%. This is because the area of a circle is proportional to the square of the radius, and tripling the radius results in an area that is nine times greater than the original area, which translates to an 800% increase.

A) 200%

Option A is incorrect because a 200% increase would only imply that the area becomes three times the original area, not accounting for the squared relationship between the radius and the area.

B) 300%

Option B is also incorrect. A 300% increase would mean the area is four times the original area, which is not the case when the radius is tripled, as the area actually becomes nine times the original.

C) 400%

Option C is incorrect as well, as a 400% increase would indicate that the area is five times the original area. This does not align with the mathematical relationship governing the area of a circle when the radius is increased.

D) 800%

Option D is correct. Tripling the radius results in the area becoming nine times larger, which equates to an increase of 800% over the original area, confirming the mathematical principle that area scales with the square of the radius.

Conclusion

In conclusion, the correct answer is 800% because tripling the radius of a circle leads to an area that is nine times the original, resulting in an increase of 800%. The other options fail to accurately represent the geometric relationship between radius and area, which is fundamental to understanding this problem.