Question

The area of piece of circular land is 616 cm square find the diameter of the circular land and also find the cost of fencing it at the rate of rupees 5 per metre

Answer 1

$given \: : \\ \\ area \: of \: circle \: = \: 616 \: {m}^{2}$




$to \: find \: radius \: we \: have \: to \: use \: the \: formula \: for \: area \: of \: circle \:$





$\bold{area \: of \: \: circle = \pi \times {r}^{2} } \\ \\ 616 \: {cm}^{2} = \pi {r}^{2} \\ \\ 616 = \frac{22}{7} \times {r}^{2} \\ \\ \frac{ 616 \times 7}{22}= {r}^{2} \\ \\ 28 \times 7 = {r}^{2} \\ \\ 196 = {r}^{2} \\ \\ r = \sqrt{196} \\ \\ \bold{r = 14 \: cm}$




$for \: fencing \: we \: have \: to \: use \: formula \: for \: circumference \: of \: circle \:$




$\bold{circumference \: of \: a \: circle \: = 2 \times \pi \times \: r } \\ \\ circumference \: of \: a \: circle \: = 2 \times \frac{22}{7} \times 14 \\ \\ circumference \: of \: a \: circle \: = \: 2 \times 22 \times 2 \\ \\ \bold{circumference \: of \: a \: circle \: = \: 88 \: {m}}$





$cost \: for \: fencing \: = 5 \: rs \: per \: m \: \\ \\ \bold{cost \: of \: fencing \: = \: circumference \: \times cost \: per \: m \: } \\ \\ cost \: of \: fencing \: = \: 88 \times 5 \\ \\ \bold{cost \: of \: fencing \: = 440 \: rs \: }$