QUESTION $3[16$ MARKS$]$

A hotel management team is planning on designing a $3$D ice block as a hotel attraction for the Christmas $2024$ celebration. As a pre$-$step and to optimize the cost, the team needs to consider the area and surface area of bounded integral on both axes for the function $y=3x^3,0x2.$ Find the

i$)$ area generated by the curve on $y-$axis.

ii$)$ surface area that is generated by revolving the curve about $x-$axis.

$[16$ Marks$]$

$[$CO$3,$ PO$1,$ C$4]$