Let P(90cosx, 90sinx)
∴pr= 100-90sinx,pq= 100-90cosx
∴spqcr=( 100-90sinx)( 100-90cosx)
= 10000-9000(sinx+cosx)+8 100 sinx cosx
Let sinx+cosx = t ∈ [1, 2]
∴sinxcosx=t2? 12
∴sPQCR=4050t2-9000t+5950,
When t= 109, the minimum value is 950m2. ..
So the answer is: 950.