A parcel delivery service has contracted you to design an open box with square base of length x cm and height y cm and a volume of 3600 cubic cm. Find the total surface area in terms of x and y. Also determine the dimensions for minimum surface area. (Round your answers correct to two decimal places if needed.) My answer for TSA is 7200/y +2xy +7200/x and for Minimum area is 2 square root of 5 |
the total surface area is x^2+4xy (because the top is open) the volume is 3600=yx^2 y=3600/x^2 surface area is x^2+4xy x^2+4x(3600/x^2) x^2+14400/x derivative of surface area is 2x-14000/x^2 set derivative equal to 0 2x-14000/x^2=0 2x^3=14000 x^3=7000 x=7000^(1/3) dimensions for minimum surface area: x=7000^(1/3)=19.13 cm y=3600/x^2=9.84 cm |