Question

a bed is in a form of a circular sector. find its radius if the area of the sector is 1000 centimeter square and its perimeter is a minimum

Answer 1

a = 1/2 r^2 θ
so,
θ = 2000/r^2

p = 2r + rθ = 2r + 2000/r

so, find where dp/dr=0