Consider a hard disk drive $($HDD$)$ with $10$ platters of $3\mathrm{.}5$ inches in diameter,

$256$ cylinders, usable capacity of $10GB,$ block size of $4KB,20\%$ gaps between blocks,

average seek time of $20ms,$ and rotational speed of $3840$ round per minute $($RPM$).$

Assume tracks occupy the outer $1$ inch of surfaces. Answer the following questions:

$($a$).$ What is the capacity of each cylinder in bytes?

$($b$).$ How many blocks are there in each cylinder?

$($c$).$ What is the average bit density of a track $($number of usable bits per inch$)?$

$($d$).$ What is the average time to read $10$ consecutive blocks on the same track?

$($e$).$ How long would it take on average to read a block on track $0($the outer most track$),$ if the head assembly is currently on track $200?$ Consider $1ms$ as the overhead to move the $\frac{r}{w}$ head to a different track, and $1ms$ to travel over every $5$ cylinders.