You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of the can (radius and height) will use the least amount of material?(Hint: The lightest can will be the can with the smallest surface area.)

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

Substitute 432π for V

Divide through by π

Make h the subject:

Surface Area (A) of a cylinder is calculated as thus:

Substitute for h in

Factorize:

To minimize, we have to differentiate both sides and set

Set

Divide through by

Cross Multiply

Divide through by 2

Take cube roots of both sides

Recall that:

Hence, the dimension that requires the least amount of material is when

step-by-step explanation:

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew