Please explain to me how to do this

Question

A steele drum in the shape of a right cicular cylinder is required to have a volume of 100 cubic feet.? 
A). Express the amount A of material required to make the drum as a function of the radius r of the cylinder. 
B).How much material is required if the drun's raduis is 3 feet?

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Answer 1

Volume of right circular cylinder is  

Where r is radius 

             h is height

Now     ( From the volume cylinder formula )

A). Surface area of right circular cylinder is A (r , h) = 

Surface area of right circular cylinder is the function r and h { A (r , h) }

But in the question asked that surface area in the function of r only so we have to eliminate the term h 

Surface area A (r) = 

                                 = 

                                 = 

Surface area in terms of radius r is  

B). Given radius  is 3 feet

   Surface Area is =  

                       = 2π(3)² + 200/3

                       =  123.21 square feet

Material required if the drum's raduis is 3 feet = 123.21 square feet