Question

The circumference of a circular garden is 220m and a path 3.5m wide runs around the garden .find the area of the path

Answer 1

$\bold{given : } \\ \\ circumference \: of \: a \: garden : \\ \\ \bold{220 \: m} \: \\ \\ \\ \\ \bold{circumference \: of \: a \: circle : } \\ \\ \bold{2 \times \pi \times r }\\ \\ 220 \: m \: = \: 2 \times \: \pi \times r \\ \\ 220 \: m \: = \: 2 \times \frac{22}{7} \times r \\ \\ r \: = \frac{220 \times 7}{22 \times 2} \\ \\ \bold{r = 35 \: m } \\ \\ \\ \\ \bold{area \: of \: the \: garden \: without \: path :} \\ \\ \bold{\pi \times {r}^{2} }\\ \\ \frac{22}{7} \times 35 \times 35 \\ \\ 22 \times 5 \times 35 \\ \\ \bold{3850 \: {m}^{2} }\: \\ \\ \\ \\ path \: is \: 3.5 \: m \: wide \: \\ \\ \bold{radius \: of \: whole \: garden : } \\ \\ r \: = \: 35 \: m \: + \: 3.5 \: m \: \\ \\ \bold{r \: = \: 38.5 \: m} \: \\ \\ \\ \\ \bold{area \: of \: the \: garden \: with \: path : } \\ \\ \bold{\pi \times {r}^{2} }\\ \\ \frac{22}{7} \times 38.5 \times 38.5 \\ \\ 22 \times 5.5 \times 38.5 \\ \\ \bold{4658.5 \: {m}^{2} }\\ \\ \\ \\ \bold{area \: of \: path : }\\ \\ \bold{area \: with \: path \: - \: area \: without \: path \:} \\ \\ 4658.5 - 3850 \\ \\ \bold{808.5 \: {m}^{2}}$