You are asked to build an open cylindrical can (i. e. no top) that will hold 171.5 cubic inches. to do this, you will cut its bottom from a square of metal and form its curved side by bending a rectangular sheet of metal.(a) express the total amount of material required for the square and the rectangle in terms of r. (b) find the radius and height of the can that will minimize the total amount of material required

The volume of a cylinder is . From the figure, the circle inside the square makes up the base, while the lateral surface area of the cylinder is the rectangle.

In terms of r, the area of the circle from the square would be  since half the square's side is r and the area of a square is the square of is side.

The area of the rectangle is 2rh. From the equation of the cylinder's volume,

, thus the area of rectangle is 

Add both areas, take its derivative, then equate to 0 to find the value of r:

    (This is the total amount of material required for the square and the rectangle in terms of r)

, substitute this value to the equation for h in terms of r.

answer is 67%

step-by-step explanation:

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk