Calculus problems.

In this project you will design an optimal soda can.

Problem

Cans of soft drinks are made from aluminum.Due to the soaring prices, the beverage company executives are looking for all possible cost-cutting measures.You are being asked to find a way to redesign the traditional can to decrease cost as much as possible.The manufacturer fills the containers with 355 cm³ of liquid and leaves 15 cm³ of open space, so the total volume of 370 cm³ must be maintained.

Part 1: Draw a Model of the Can

1.Sketch a right circular cylinder and label the radius, r, and height, h.Give the formulas for volume and surface area of a right circular cylinder.What quantity is known? Take a picture of your work/drawing and include it here.

\fh h = height of can r = radius of can v = volume of the can = 370cm^3 volume is known GIVEN THAT VOLUME OF THE CAN IS 370cm LET, the radius of the cylinder be r Height of the cylinder be h .'. volume = arch = 370 From this equation we find the height / 370 h = 7 7-2. -(1)a) SURFACE AREA OF CYLINDER = A = 2xrh + 272 370 h = USING 72 IN THE SURFACE AREA OF THE CYLINDER 370 A = 2arh + 2arz = 2ar( + 2072 740 A =\f