Question

A circular disc's radius is decreased by 10%. What is the percentage decrease in its area?

• A. 10%
• B. 19%
• C. 18%
• D. 15%

Answer 1

Answer:

B. 19%

Area of a circle is proportional to the square of the radius.

If the radius decreases by (10%), the new radius becomes:

$90\% = 0.9r$

New area:

$0.9r^2 = 0.81r^2$

So the new area is (81%) of the original area.

Percentage decrease:

$100\% - 81\% = 19\%$

Therefore, the area decreases by:

$\boxed{19\%}$