Question

If the circumference of a circle increases from $4\pi$ to $8\pi$ what change occurs in its area?

• A. Change = $2\times$ Original area
• B. Change = $3\times$ Original area
• C. No change
• D. Change = $4\times$ Original area

Answer 1

The correct option is B Change = $3\times$ Original area

Radius of the circle before change $=\frac{4\pi }{2\pi }=2units$
$\therefore$ Area of the circle before change $=\pi (2{)}^{2}squnits$
$=4\pi squnits$
Raduis of the circle after change $=\frac{8\pi }{2\pi }=4units$
$=16\pi squnits$
change in area $16\pi -4\pi =12$ $\pi$ $=3\times 4$ $\pi$
= 3 x Original Area