Question

A road which is 7meter wide surrounds a circular path whose circumference is 352m. Find the area of the road

Answer 1

A road which is 7meter wide surrounds a circular path whose circumference is 352m. Find the area of the road

Answer 2

$\bf{ \pmb{GIVEN:-}} \\ \sf \: Width \: of \: the \: road=7m \\ \sf \: Circumference \: of \: circular \: park=352 m \\ \\ \\ \pmb{ \bf{TO \: FIND \: OUT:-}} \\ \sf Area \: of \: the \: road \\ \\ \\ \pmb{ \bf{SOLUTION:-}} \\{\sf Let \: the \: radius \: of \: the \: park \: be \: }r \sf \: m \\ \\ \bf \: Then \: its \: circumference =2 \pi r \\ \therefore \rm \: 2 \pi r=352 \\ \rm \: 2 \times \frac{22}{7} \times r = 352 \\ \rm \: r = \huge( \small352 \times \frac{7}{44} \huge) \small \: = 56 \\ \\ \sf Thus , \: inner \: radius=56m \\ \sf \: outer \: radius = (56 + 7)m = 63m \\ \\ \\ \sf Area \: of \: road= \pi \: [(63)²-(56)²]m² \\ \\ \rm \frac{22}{7} \times (63 + 56)(63 - 56)m {}^{2} \\ \\ \rm \huge( \small \frac{22}{7} \times 119 \times 7 \huge) \small \: m {}^{2} = 2618m ^{2} \\ \\ \boxed {\bf \therefore \: Required \: area \: of \: road=2618m {}^{2} }$