Volume of a cylinder: v=πr to the power of 2 h;solve for h

V = π * r2 * h, and r + h = 12

You have 2 independent variables, so use both equations to develop a formula for V. It seems best to use substitution for h, to keep the equation relatively simpleSo:

r + h = 12

rearrange to get: h = 12 - r

Substitute in the 1st equation to get:

V = π * r2 * (12 - r)

Expand:

V = 12πr2 - πr3

To find a maximum (or minimum), the typical method is to find the 1st derivative and set it equal to zero.

V' = 24πr - 3πr2

Set equal to 0 and solve for r:

24πr - 3πr2 = 0

8r - r2 = 0

r = 0, 8 (Interpretation: 0 gives you the minimum volume, and 8 gives you the maximum)

Step-by-step explanation:

hope this will help you

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet