Question

A circular track has a circumference of 176m. Find the area of the path of width 4m inside it.

Answer 1

hello aysha!
the circumference of the track is given as 176m
so by the formula for circumference, we get, 2$\pi$r=176
so by putting the value of pi as 22/7, we can get the radius
and the radius comes out to be 28m
now that we have the radius of the circle , we can find it's area by using
area of circle= $\pi$r^2
so we get the are of the circle as 2464m^2
but what is asked is the area of the track that is formed by this big sircle and a small circle of radius 4m
so we gotta reduce the area of the smaller circle to get the are of the track formed by these circles
so it'll go like this
area of track= 2464 - area of smaller circle
again you need to use the formula for are of the circle to find the area of the smaller circle
you'll get the area of the smaller circle 50.16m^2
so area of the track = 2464-50.16 = 2413.84m^2 and this may be the final answer
if you have any querries , feel free to ask!
i hope this helps you:)

Answer 2

DATA : circumference= 176m
ie 2*(22/7)*r=176
R=28
4m wide so inner circle radius=28-4
r=24m
now area of circle=radius*radius(22/7)
Area of R -Area of r
(22/7)((28*28)-(24*24))
=(22/7)(784-576)
=(22/7)*(208)
=653.71428m