Question

a circular garden has a area 4 m wide path around it. find the radius of the garden if the area is 1408m^2​

Answer 1

Let r = radius of the garden

width of the path = 4 m

area of the path = 1408 m​^2

Let R = radius of outer circle

Now, width of the path = 4 m

⇒⇒R - r = 4      ........(1)

area of the path = 1408 m^2

⇒πR^2 − πr^2 = 1408

⇒π[R^2 − r^2] = 1408

⇒227(R + r) (R − r) = 1408

⇒(R + r) (R − r) =1408×722

⇒(R + r) (R − r) =448

⇒(R + r)(4) = 448

⇒R + r = 112         .......(2)

adding (1) and (2), we get

2R = 116

⇒R = 58 m

from (1), we get

r = 58 − 4 = 54 m