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6 Nov 2019
Folded boxes
Folded boxes Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. Suppose that in part (a) the original piece of cardboard is a square with sides of length l. Find the volume of the largest box that can be formed in this way. Suppose that in part (a) the original piece of cardboard is a rectangle with sides of length l and L. Holding l fixed, find the size of the corner squares x that maximizes the volume of the box as L rightarrow infinity. (Source: Mathematics Teacher, November 2002) Making silos A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 1.5 times as mu Ch as the concrete (per unit of Show transcribed image text
Folded boxes
Folded boxes Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way. Suppose that in part (a) the original piece of cardboard is a square with sides of length l. Find the volume of the largest box that can be formed in this way. Suppose that in part (a) the original piece of cardboard is a rectangle with sides of length l and L. Holding l fixed, find the size of the corner squares x that maximizes the volume of the box as L rightarrow infinity. (Source: Mathematics Teacher, November 2002) Making silos A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 1.5 times as mu Ch as the concrete (per unit of
Show transcribed image text Lelia LubowitzLv2
7 Sep 2019