Shape Reading
What are the radius and height of the least expensive can in a cylinder shape? READ THE DETAILS!?
Material for curved surfaces is twice as much per cm2 as material for top and bottom. Also the volume will equal 500 cm3
Ps. Dont give me the answer, just a way of solving it or an equation wud be nice
Let
Let
Cs = cost of the curved surface of the cylinder
Cf = cost of the flat surface (top or bottom)
Total cost of of cylinder = C = Cs(As) + 2Cf(Af)
where
C = total cost of cylinder
As = area of curved surface of cylinder
Af = area of the flat surface (top or bottom)
since Cs = 2Cf, then the above formula for cost simplifies to
C = 2Cf(As) + 2Cf(Af)
C = 2Cf(As + Af)
As = 2pi(R)(H)
and
Af = pi(R^2)
where
R = radius of the cylinder
H = height of the cylinder
C = 2Cf[2(pi)(RH) + (pi)(R^2)] --- call this Equation C
The volume of the cylinder is equal to
500 = pi(R^2)(H)
and solving for H,
H = 500/(pi*R^2) and substituting this into Equation C,
C = 2Cf[2(pi)(R)(500/(pi)(R^2) + (pi)(R^2)]
Simplifying the above,
C = 2Cf[1000/R + (pi)R^2]
I will stop my actual solution here. I will outline the rest of the steps in the solution of this problem.
Step 1 -- differentiate the above equation
Step 2 -- set the derivative equal to zero
Step 3 -- solve for "R"
Step 4 -- after solving for "R", solve for "H" using the formula
H = 500/(pi*R^2)
Hope this helps.
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