Question

If the diameter of a circle is decreased by 10%, calculate the percentage decrease in the area of the circle? (round off to 2 decimal places)

• A. 17.5%
• B. 19%
• C. 9.75
• D. 10.25%

Answer 1

The correct option is B 19%

Let the initial diameter of the circle be 'd' ft.
$\text{Initial Area =}\frac{𝛑}{4}{d}^2$

New diameter = 90% of d

$=\frac{90}{100}d$

$=0.9d$

$\text{Final Area of circle =}\frac{𝛑}{4}(0.9d{)}^2$
$=0.81\frac{𝛑}{4}{d}^2$

$\text{Percenatge change in area =}\frac{Finalarea-Initialarea}{Initialarea}\times 100\%$

$=\frac{0.81\frac{𝛑}{4}{d}^2-\frac{𝛑}{4}{d}^2}{\frac{𝛑}{4}{d}^2}$

$=-\frac{0.19\frac{𝛑}{4}{d}^2}{\frac{𝛑}{4}{d}^2}$

$=-19\%$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴ The percentage decrease in area of the circle is 19%.