Provide a FULL SOLUTION to Question #1 1) A cylindrical tin with a capacity of 750 cm3 is to be constructed out of sheet metal. The construction material for the side and base costs $ 0.05/cm2 and for the top costs $0.10/cm2. The tin must fit into premade boxes with a base of 14 cm by 14 cm and a height of 5 cm. Determine the dimensions of the tin, to two decimal places, that will minimize the cost of the metal needed.

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.