Mathematics, 02.02.2020 18:46, andrewbao999
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
Answers: 3
. From the figure, the circle inside the square makes up the base, while the lateral surface area of the cylinder is the rectangle.
since half the square's side is r and the area of a square is the square of is side.
rh. From the equation of the cylinder's volume,
, thus the area of rectangle is 
(This is the total amount of material required for the square and the rectangle in terms of r)
![[8r- \frac{343}{ r^{2}}=0] r^{2}](/tpl/images/0493/5776/1011c.png)
, substitute this value to the equation for h in terms of r.
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You are asked to build an open cylindrical can (i. e. no top) that will hold 171.5 cubic inches. to...
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