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Mathematics
Mathematics
Problem
For
k
>
0
k>0
k
>
0
, let
C
k
C_k
C
k
be the quarter–circle arc defined by
y
=
k
2
−
x
2
y=\sqrt{k^{2}-x^{2}}
y
=
k
2
−
x
2
for
0
≤
x
≤
k
0\le x\le k
0
≤
x
≤
k
. If the length of
C
k
C_k
C
k
is
π
\pi
π
units, what is the value of
k
k
k
? a)
4
4
4
b)
π
2
\dfrac{\pi}{\sqrt{2}}
2
π
c)
2
2
2
d)
1
1
1
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