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- A metal storage tank with fixed volume V0 = 360π m^3is to be constructed in the shape of a right circular cylinder (including the bottom) surmounted by a hemisphere. A picture is given below.What dimensions will require the least amount of metal? Show and organize your work; use the firstderivative test or the second derivative test or other tools to check that yours is the desired optimalsolution.Exact reducibleWith the use of examples, differentiate between horizontal integration andvertical integration.
- solve the problem with the second partial derivative test or with Lagrange's method: Find the volume of a rectangular box with maximum volume if the surcafe is 96cm2 please show full and complete procedure HANDWRITTEN onlyDefinite Integ.FIND THE CENTROID OF THE REGION IN THE FIRST QUADRANT BOUNDED BY THE GRAPH OF y=9-x2, THE X-AXIS, AND THE Y-AXIS (SOLVE BY USING INTEGRAL CALCULUS)