Izuddin has a rectangular piece of zinc with a perimeter of 32 cm. He wants to use that
piece of zinc to build an open cylinder at both ends.
Find the length and the width, in cm, of the piece of zinc that makes the volume of the
cylinder is maximum. help me solve thank you. answer for length is 12 width 4

Length is 10 2/3 width is 5 1/3 cm.

Step-by-step explanation:

The 32 cm perimeter is equivalent to  2 * circumference of the cylinder + 2  * the height.

2C + 2h = 32.

Now C = 2πr, so

2*2πr + 2h = 32

4πr + 2h = 32

2h = 32 - 4πr

h = 16 - 2πr.

Volume of the cylinder = πr^2h, so

V = π(16 - 2πr) r^2

V = 16πr^2 - 2π^2r^3

Finding the derivative:

V' =   32πr - 6π^2 r^2     This = 0 for a maximum volume:

32πr - 6π^2r^2 = 0

2πr(16 - 3πr) = 0

16 - 3πr = 0

r = 16/3π.

So the circumference = 2π *  16/3π = 32/ 3 = 10 2/3 cm.

The height = 16 - 10 2/3 = 5 1/3.

Therefore the width of the zinc is 5 1/3 and the length is 10 2/3.

answer is d-29

step-by-step explanation:

since you didn't include the picture, i can give you the description so you know how to pick the correct answer. the third quartile of a data is always shown in a box plot. in the middle of your graph should be a box. the third quartile is the value that goes with the far right edge of the box.