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1. If the radius of a circle is decreased by 20% then the area is decreased by:

  • A. 20%
  • B. 20%
  • C. 20%
  • D. 20%

Answer: Option C

Explanation:

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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