Question

a road which is 7m wide surrounds a circular park whose circumference is 352m .find the area of the road.

Answer 1

hi friend
here's your answer looking for

circumference of the park =

$2 \: \pi \: r \: = 352 \\ \\ 2 \times \frac{22}{7} \times r = 352 \\ \\ r = \frac{352 \times 7}{44} \\ r = 56m$
now,

area of park =

$\pi \: {r}^{2} \\ \\ = \frac{22}{7} \times 56 \times 56 \\ \\ = 9856 {m}^{2}$
now,

area of park along with road =

$\frac{22}{7} \times (56 + 7)(56 + 7) \\ \\ = \frac{22}{7} \times 63 \times 63 \\ \\ = 12914 {m}^{2}$
finally,

area of road =
$12914 - 9856 \\ \\ = 3058 {m}^{2}$
so this is your answer

hope you are satisfied with my answer

Answer 2

GIVEN:-

•Width of the road=7m

•Circumference of circular park=352 m

TO FIND OUT:-

$\bf \:• Area \: of \: the \: road=?$

SOLUTION:-

$\bf \:$

${\bf •Let \: the \: radius \: of \: the \: park \: be \: }r \bf \: m$

$\bf \: •Then \: its \: circumference =2 \pi r$

$\therefore \bf \: 2 \pi r=352$

$\bf \implies \: 2 \times \frac{22}{7} \times r = 352$

$\bf \implies \: r = \huge( \small352 \times \frac{7}{44} \huge) \small \: = 56$

$\bf •Thus , \: inner \: radius=56m$

$\bf \to \: outer \: radius = (56 + 7)m = 63m$

$\bf Area \: of \: road= \pi \: [(63)²-(56)²]m²$

$\bf \: \: \: \: \: \: = \frac{22}{7} \times (63 + 56)(63 - 56)m {}^{2}$

$\bf \: \: \: \: \: \implies \huge( \small \frac{22}{7} \times 119 \times 7 \huge) \small \: m {}^{2} = 2618m {}^{2}$

$\boxed{\boxed {\bf \therefore \: Required \: area \: of \: road=2618m {}^{2} }}$