Question
The radius of a circle is tripled. Which of the following
describes the effect of this change on the area?
describes the effect of this change on the area?
Ask by Burns John. in the United States
Mar 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Tripling the radius of a circle increases its area by a factor of 9.
Solution
Let the original radius of the circle be
When the radius is tripled, the new radius becomes
This shows that the new area is 9 times the original area.
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Simplify this solution Beyond the Answer
When the radius of a circle is tripled, the area of the circle increases by a factor of nine! This is because the area of a circle is calculated using the formula A = πr². If you replace r with 3r, you get A’ = π(3r)² = 9πr². Essentially, you’re creating quite the party for your circle—three times the radius means nine times the fun!
In the real world, this concept is particularly useful in various fields like urban planning and landscaping. For example, if a city doubles the radius of a park, the area expands significantly, allowing for more trees, playgrounds, and picnic spots! Urban planners need to understand these area changes to maximize green spaces for the community.
