Question

A path runs around a circular grass field with uniform width of 2 meters outside it.If the circumference of the field be 24pi m,then the area of the path (taking pi=3.14) is

Answer 1

circumference = 2pir = 24pi
2r = 24
r o f the field = 12
r including the path = 14
to find the area of the path, pi(14)^2 - pi(12)^2

615.44 - 452.16
= 162.98 m^2

Answer 2

The area of the path is 163.28  sq.m

Step-by-step explanation:

Given Width of the path around the grass field is 2 m.  

Also circumference of the field given is 24Π

2Πr = 24Π

r = 12 m

Therefore, radius of the field including the grass field and path of width 2 m is,

12 + 2 = 14

$\Rightarrow \text { Area of the outer circle }=\pi \times 14^{2}=196 \pi$

$\Rightarrow \text { Area of the inner circle }=\pi \times 12^{2}=144 \pi$

$\text{Area of the required path of width 2 m} = \text{Area of outer circle} - \text{Area of inner circle}$

$=196 \pi-144 \pi$

$=52 \pi$

$=52 \times 3.14$

$\therefore \text { Area of the required path of width } 2 m=163.28 \ \mathrm{sq.m}$