$($a$)$ A man weighing $791$ N lies on a bed of nails. Find the average pressure exerted by a nail on his skin if there are $1010$ nails and the flattened point on each nail has a radius of $0\mathrm{.}500$ mm$.$

$($b$)$ Calculate the pressure exerted on the skin by an acupuncture needle of radius $0\mathrm{.}100$ mm applied with a force of $4\mathrm{.}40$ N$.$