A disk has $800$ tracks per surface, $180$ sectors per track, and $512$ bytes per sector. The disk has $1$ surface. The disk rotates at $5000$ rpm $($rotations per minute$).$ The average seek time between random tracks is $10$ ms$.$ The seek time between adjacent tracks is $2$ ms$.$

$($a$)$

Determine the total storage capacity of the disk.

$($b$)$

Determine the number of seek operation to read the entire disk.

$($c$)$

Determine the peak data rate of the disk $($MB$/$second$).$

$($d$)$

If the r$/$w head is at track i$,$ how long will it take to read a sector on track i $+1?$

$($e$)$

Determine the sustained data rate of the disk for accessing blocks distributed randomly over the disk $($MB$/$second$).$