Question #4ef82

1 Answer
Feb 5, 2018

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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