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

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by AyshaJasra

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by AyshaJasra

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the circumference of the track is given as 176m

so by the formula for circumference, we get, 2r=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= 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:)

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