If the radius of a circle is tripled, by what percent is the area of the circle increased?

Rationale

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 a factor of nine, which translates to an 800% increase from the original area. This is due to the area formula \( A = \pi r^2 \), where tripling the radius results in \( A' = \pi (3r)^2 = 9\pi r^2 \).

A (200%) YOUR ANSWER

This choice suggests that the area increases by only double the original area, which is incorrect. A 200% increase would imply that the new area is three times the original area, but this does not reflect the actual calculation when the radius is tripled.

B (300%) YOUR ANSWER

Choosing 300% indicates the new area would be four times the original area, which also misrepresents the relationship between radius and area. The area actually increases by a factor of nine, not four, when the radius is tripled.

C (400%) YOUR ANSWER

This option implies that the new area is five times the original area, representing a 400% increase. While an increase of this magnitude might seem significant, it falls far short of the actual ninefold increase resulting from tripling the radius.

D (800%) CORRECT

This is the correct response, as tripling the radius results in an area that is nine times larger than the original. The percentage increase is calculated as \( \frac{9 - 1}{1} \times 100\% = 800\% \).

Conclusion

The relationship between the radius and the area of a circle demonstrates a quadratic nature, meaning that changes in the radius have a multiplicative effect on the area. Thus, when the radius is tripled, the area increases to nine times its original size, reflecting an 800% increase. Understanding this relationship is crucial in geometry and applications involving circular shapes.

If the radius of a circle is tripled, by what percent is the area of the circle increased?

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

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test