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The area of a two-dimensional region can be calculated using the aforementioned definite integral. The volume of a three-dimensional object such as a disc or washer can be computed by disc integration using the equation for the volume of a cylinder, , where is the radius.

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An open topped container, in the shape of a cylinder with a circular base, is to be made from strong thin sheet-metal of negligible thickness. The container must hold 1 m^3 and its outer surface area must be kept to a minimum to reduce the cost of the manufacture. Calculate in m^2 (to 3.d.p) the minimum surface area ? Please help.

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Because of the open top, the formula for the surface area is pi*r^2 + 2*pi*r*h = 8 Solving for height, H = (8-pi*r^2)/(2*pi*r) <--- call this equation H Substituting this for the height in the formula for the volume of a cylinder:

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The surface area is the total area of the curved surface and the bases.Lateral Area: The lateral area of a right cylinder with radius r and height h is L = 2pirh.Surface Area: The surface area of ...

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where is the angle between the magnetic field and the area vector . The area vector has a magnitude equal to the area of a surface, and a direction perpendicular to the plane of the surface. The SI unit for magnetic flux is the weber (Wb). 1 Wb = 1 T m2. EXAMPLE 20.1 – Determining the magnetic flux

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Initially, the graduated cylinder contains 40 ml of water. As the object enters the water, the top surface of the water moves up. The volume of the displaced water is equal to the increase in volume. Initial graduated cylinder reading = 40 ml Reading with object in the water = 48 ml Volume of the displaced water = 48 – 40 = 8 ml