Problem $1.(20$ points$)$:

Consider a disk with the following characterigics $($these are not parameters of any particular disk unit$)$; block size $\backslash (\backslash$mathrm$\{$B$\}=512\backslash )$ bytes, number of blocks per track $\backslash (=50\backslash ).$ number of uacks per surface $\backslash (=200\backslash ).$ A disk pack consists of $10$ double$-$sided disks. $($Note: in this problem, interblock gap is ignored und do not need to be considered.$)$

$($a$)$ What is the totel capacity of a track?

$($b$)$ How many cylinders are there?

$($c$)$ What is the total capwity of the entire disk?

$($d$)$ Stippose the disk frive rotates at a speed of $3000$ rpm $($revolutions per minute$)$; what is the block transfer time brt in msec? What is the average rotational delay rd in mee?

$($c$)$ Suppose the average seek time is $40$ misec. How much time does it take $($on the uverage$)$ in msec to locate Ind transfer a single block given its block address? $($basing on the rd and bre you calculated in problem d$)$

$($f$)$ Calculate the average time it would take to transfer $10$ random blocks and compare it with the time it would take to transfer $10$ consecutive blocks. $($basing on the assumptions in problem dand e$)$