Question

If the radius of a circle is decreased by 50%.
Find the percentage decrease in its area.​

Answer 1

75%

Step-by-step explanation:

$area \: of \: circle \: = \pi {r}^{2} \\ new \: radius \: = \: 50\% \: of \: r \\ = \frac{r}{2} \\ new \: area \: = \pi { (\frac{r}{2}) }^{2} \\ = \pi \frac{ {r}^{2} }{4} \\ \% \: decrease \: in \: area \: = \frac{\pi {r}^{2} - \pi \frac{ {r}^{2} }{4}}{\pi {r}^{2}} \times 100\% \\ = \frac{\frac{3}{4} \pi {r}^{2} }{ \pi {r}^{2}} \times 100\% \\ = \frac{3}{4} \times 100\% \\ = 75\%$