Question

the effect on the area of the circle if the radius is doubled.

• A. Area becomes 2 times.
• B. Area becomes 8 times.
• C. Area becomes 6 times.
• D. Area becomes 4 times.

Answer 1

The correct option is D Area becomes 4 times.

$Given-thecircumferenceCofacircle=r=123.2cm.Theradius=risdoubledTofindout-theeffectontheareaofthecircle=?$

$Solution-ThecircumferenceCofthecircle=2\pi r$

$\Rightarrow r=\frac{C}{2\pi }=\frac{123.2}{2\times \frac{22}{7}}cm=\frac{123.2\times 7}{2\times 22}cm=19.6cm.Nowar.circle=\pi r^2=\frac{22}{7}\times {19.6}^2{cm}^2=1207{cm}^2.Nowtheradiusisdoubled$

$\therefore thenewradius=2r=2\times 19.6cm=39.2cm.Sothenewareaofthecircle=\frac{22}{7}\times {39.2}^2{cm}^2=4828{cm}^2.$

$\therefore \frac{newarea}{originalarea}=\frac{4828}{1207}=4:1i.etheareawillbe4timestheoriginalarea.$

$[NOTE-Theproblemcanbesolvedinanotherway.Theoriginalarea=\pi r^2.Thenewradius=2r.\therefore Thenewarea=\pi {\left(2r\right)}^2=4{\pi r}^2.\therefore \frac{newarea}{originalarea}=\frac{4{\pi r}^2}{{\pi r}^2}=4.i.etheresultdoesnotdependuponthedata.]$

$Ans-OptionD.$