A race track is in the shape of a ring whose inner and outer circumferences are 880 m and 1012 m, respectively. What is the area (in m
2
) of the track? (Take π=
7
22
​
)

Let the outer radius be R and the inner radius be r.
Inner circumference:

2πr=880⟹2×
7
22
​
×r=880⟹r=
44
880×7
​
=140 m
Outer circumference:

2πR=1012⟹2×
7
22
​
×R=1012⟹R=
44
1012×7
​
=163 m
The area of the track is given by:

Area=π(R
2
−r
2
)=π(R−r)(R+r)
Area=
7
22
​
×(163−140)×(163+140)
Area=
7
22
​
×23×303
We know that 163−140=23, wait, let's calculate carefully:

Area=
7
22
​
×23×303=19866 m
2