I am solving question (11).
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11. Determine the dimensions of a rectangular solid with a square base that maximizes the volume...
A rectangular solid (with a square base) has a surface area of 73.5 square centimeters. Find the dimensions that will result in a solid with maximum volume. cm (smallest value) cm cm (largest value)
A rectangular tank with a square base, an open top, and a volume of 6912 n° is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. The dimensions of the tank with minimum surface area aren. (Simplify your answer. Use a comma to separate answers.)
A rectangular tank with a square base, an open top, and a volume of 884 ft is to be constructed of sheet steel Find the dimensions of the tank that has the minimum surface area n& Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective tunction A- Type an expression.) The interval of interest of the objective function is tiond (Simplity your...
A rectangular tank with a square base, an open top, and a volume of 864 n is to be constructed of sheet stoel. Find the dimensions of the tank that has the minimum surface area, Lets be the length of one of the sides of the square base and let A be the surface area of the tank. Write the primary equation in terms of A-O (Type an expression.) The domain of the primary equation is (Simplify your answer. Type...
A box with a square base and open top must have a volume of 2048 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. The length of the base is x and the height is h. Since the base is a square, the surface area of just the base would be: Area = The surface area of just one side would be: Area = The surface area of all...
All boxes with a square base, an open top, and a volume of 200 ftº have a surface area given by S(x)=x2 + where x is the length of the sides of the base. Find the absolute minimum of the surface area function on the interval (0,00). What are the dimensions of the box with minimum surface area? Determine the derivative of the given function S(x). S'(x)=0 The absolute minimum value of the surface area function ist? (Round to three...
Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 54 ft3. If the material for the base costs $0.22/ft2, the material for the sides costs $0.09/ft2, and the material for the top costs $0.14/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost. (Refer to the figure below.) A closed rectangular box has a length of x, a width of x, and a height of y. x=?...
Calculate the surface area and volume of a rectangular solid measuring 43mm in length, 12mm in width, and 19mm in height (report your answer in cm square and cm cube). The mass of this block is 8.4g. What is it's density and will it sink or float in water?
A box with a square base and open top must have a volume of 296352 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. A(x) = Next, find the derivative, A'(x). A'(x) = The critical value is 3 = The function is decreasing ✓ until the critical...
Y 240 All boxes with a square base, an open top, and a volume of 60 ft have a surface area given by S(x)= x2 + where x is the length of the sides of the base. Find the absolute minimum of the surface area function on the interval (0,00). What are the dimensions of the box with minimum surface area? Determine the derivative of the given function S(x). 240 S'(x) = 2x- The absolute minimum value of the surface...