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SOLVED: The diagram shows a square prism of length L cm and cross-section x cm by x cm. Given that the surface area of the prism is k cm², where k is constant, k-2r², show that / = (k/2x)^(1/2). Use calculus to prove that the maximum volume of the prism occurs when it is a cube.
2023年11月28日
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A rectangular prism is 4 units high, 2 units wide, and 6 units long. What is its surface area in square units? Explain or show your reasoning. | Numerade
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SOLVED: The base of a right triangular prism has an area of 98 square units. If the total surface area of the prism is 466 square units, which of the following are possible areas for the faces of the prism? 30, 110, and 90 square units 40, 80, and 120 square units 50, 100, and 150 square units 60, 90, and 120 square units
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A curved prism has a base which is a sector of a disk of radius r inches and central angle θradians. The prism extends vertically to a height of h inches. (a) Derive formulas for the volume V, in cubic inches, and the total surface area (including the top and bottom) A, in square inches. (b) If V is required to be 27 , what values of r, θ, and h minimize the surface area A of the prism? | Numerade
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