Question

You plan to build a cylindrical container with no top. The material used for the lateral sides costs $4 per square foot while the material for the bottom costs $5 per square foot.
a) Express the total cost of building the cylinder, C in terms of the cylinder's radius, r, and height, h.
C= ___________
b) If the volume of the cylindrical container is 250 cubic feet, express the total cost of building the cylinder, C in terms of the cylinder's radius, r.
C(r)=__________

Answer 1

A) C = $8.pi.h.r + $5.pi.r^2

Assuming pi is 3.14, then C is $25.12.h + $15.7.r^2

The formula of the total of the cylindrical is (without top) = (height x 2 x pi x radius) + (pi x radius^2 )

So in this case, the total cost is = $4.h.C.pi + $1.25.h.C

B) r.C(r)= square root of (250 / (pi x h.C))

The formula for cylindrical volume = pi x r.C^2 x h.C