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1. If an open box is made from a tin sheet 10 in. square bycutting out identical squares from each corner and bending up theresulting flaps, determine the dimensions of the largest box thatcan be made. (Round your answers to two decimal places.)

height_____ in

length _____ in

width_____ in

For its beef stew, Betty Moore Company uses aluminumcontainers that have the form of right circular cylinders. Find theradius and height of a container if it has a capacity of 35 in.3and is constructed using the least amount of metal. (Round youranswers to two decimal places.)

radius _____in

height _____ in

If an open box is made from a tin sheet 10 in. square bycutting out identical squares from each corner and bending up theresulting flaps, determine the dimensions of the largest box thatcan be made. (Round your answers to two decimal places.)

height _____in

length_______ in

width _______in

A wooden beam has a rectangular cross section of height h in.and width w in. (see the accompanying figure). The strength S ofthe beam is directly proportional to its width and the square ofits height. What are the dimensions of the cross section of thestrongest beam that can be cut from a round log of diameter d = 28in.? (Hint: S = kh2w, where k is a constant of proportionality.Round your answers to one decimal place.) W= ______in , H=_______in.