If the radius of a circle is decreased by 15%. By what percent area of the circle decrease?

Correct option is B

Given:

The radius of the circle is decreased by 15%.

Formula Used:

The area of a circle is given by the formula:

A = $$\pi r^2$$​​

where r is the radius of the circle.

Solution:

Let the initial radius be r and the initial area be A = $$\pi r^2.$$​​

If the radius is decreased by 15%, the new radius becomes:

​$$r_{\text{new}} = r \times (1 - 0.15) = 0.85r$$​​

​$$A_{\text{new}} = \pi (0.85r)^2 = \pi \times 0.7225r^2$$​​

Percentage decrease in area = $$\left( 1 - 0.7225 \right) \times 100 = 0.2775 \times 100 = 27.75\%$$​​

The area of the circle decreases by 27.75%.

Thus the correct option is (b)  27.75%

Alternate Method:

15% = $$- \frac{3}{20}$$ ; A $$\propto$$ (Radius)²​

Old          New

Radius →     20              17

Area →       400             289

Percentage decrease in area = $$\frac{400 - 289}{400} \times 100\%$$ 

= $$\frac{111}{4} \%$$ = 27.75%​