Question
A circle has a radius of 12 cm . If the area is multiplied by 25 ,
what happens to the radius?
what happens to the radius?
Ask by Parsons Huff. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
When the area of the circle is multiplied by 25, the radius increases from 12 cm to 60 cm.
Solution
-
The area of a circle is given by the formula
-
For the original circle with radius
cm, the area is -
When the area is multiplied by 25, the new area becomes
-
Let the new radius be
. Using the area formula for the new circle, we have Dividing both sides by, we get -
Taking the square root of both sides, we find
Thus, when the area is multiplied by 25, the radius increases from 12 cm to 60 cm.
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Simplify this solution Mind Expander
When you multiply the area of a circle by 25, the radius actually changes in a way that might surprise you! The area of a circle is given by the formula A = πr². If the area is multiplied by 25, you’re really looking at how that impacts the radius.
To find the new radius, you take the square root of the area change: if the original radius is 12 cm, then the new area is 25 times larger, so you would take the square root of 25, which is 5. Since the original radius is 12 cm, the new radius becomes 12 cm x 5 = 60 cm! That’s one big circle!
