If the radius of a circle is decreased by 20% then the area is decreased by:
Created: 2 years ago |
Updated: 8 months ago
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When the radius of a circle is decreased by 20%, the new radius becomes 80% (100% - 20%) of the original radius.
Let's denote the original radius as "R" and the new radius as "0.8R" (80% of R).
Now, let's calculate the areas of the original circle and the new circle:
- The area of the original circle with radius R is πR^2.
- The area of the new circle with radius 0.8R is π(0.8R)^2.
To find the percentage decrease in the area, we can compare the areas of the new and original circles:
(π(0.8R)^2 - πR^2) / (πR^2) * 100%
Simplify:
[(0.8R)^2 - R^2] / R^2 * 100%
Now, calculate:
[(0.64R^2 - R^2) / R^2] * 100%
Simplify further:
[(-0.36R^2) / R^2] * 100%
The R^2 terms cancel out:
-0.36 * 100%
So, the area is decreased by 36%. Therefore, the correct answer is 36%.
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