Acylindrical metal container, open at the top. is to have a capacity of 24pi cu. in. the cost of material used for the bottom of the container is $0.15/sq. in., and the cost of the material used for the curved part is $0.05/sq. in. find the dimensions that will minimize the cost of the material, and find ihe minimum cost.

x  =  2,94  ft

h  = 0,88  ft

C(min)  =  12,23 $

Step-by-step explanation:

Let x be radius of the base and  h th hight of th cylinder  then

Area of the bottom    A₁   = π*x²

And cost of the bottom   C₁  = 0,15*π*x²

Lateral area A₂

A₂  =  2*π*x*h               but     V  =  24 ft³       V  = π*x²*h      h = V/ π*x²

A₂  =  2*π*x* (24/ π*x²)

A₂   =  48 /x

Cost of area A₂

C₂   =  0,05 * 48/x  

C₂   = 2,4/x

Total cost C                   C   =   C₁   +   C₂

C(x)  =  0,15*π*x²  +  24/x

Taking derivatives on both sides of the equation

C´(x)  =  0,3**π*x   -  24/x²

C´(x)  = 0               0,3**π*x   -  24/x²  =  0

0,942 x³   =  24

x³    =   25,5

x  =  2,94  ft     and    h  =  V/π*x²        h  =  24 /3,14* (2,94)²

h  = 0,88  ft

C(min)  =  0,15 * 3,14 * (2,94)²    +   24/2,94

C(min)  =  4,07   +  8,16

C(min)  =  12,23 $

what are the things "represented below"?

step-by-step explanation:

nobody can if you dont give the choices

the answer is:

the lateral area is equal to

to find the lateral area of the square pyramid, first we need to find the perimeter of the base, and then, find the lateral area using the following formulas:

where,

s, is the base length

slant height, is the height of a the side of the pyramid

we are given:

now, calculating the perimeter of the base, we have:

then, calculating the lateral area:

hence, we have that the lateral area is equal to

have a nice day!