It is revealed from the above figure that surface area of the cyndrical solid with a conical cavity will be
#A=2pirh+pirl+pir^2#
#=>A=pir(2h+l+r)#
Given
Total surface area of the solid #A=904.32dm^2#
Height of the solid #h=16dm#
Radius #r=6dm#
Density #rho=7.5g"/"cm^3=7.5kg"/"dm^3#
The slant height #(l)# of the cone is not known.
So
#904.32=3.14xx6(2xx16+l+6)#
#=>l+38=(904.32)/(3.14xx6)=48#
#=>l=48-38=10dm#
So height of the conical cavity will be
#h_"cone"=sqrt(l^2-r^2)#
#=>h_"cone"=sqrt(10^2-6^2)=8dm#
Now volume of the solid
#V="volume of cylinder"-"volume of cavity"#
#=pir^2h-1/3pir^2h_"cone"#
#=pir^2(h-h_"cone"/3)#
So weight (mass) of the solid will be
#W=Vxxrho#
#=>W=Vxxrho=pir^2(h-h_"cone"/3)rho#
#=>W=3.14xx6^2(16-8/3)xx7.5kg#
#=>W=3.14xx36xx40/3xx7.5kg=11304kg#
