Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function . Graph the function. What is the maximum volume for the domain ? Round to the nearest cubic foot. a107 ft3 b105 ft3 c10 ft3 d110 ft3

an open box is to be made from a 15ft by 40ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have round answer to nearest integer the maximum volume is blank ft^3

If 22700cm of material is available to make a boxwith a square base and an open top, find thedimensions (length, width, and height) of the box thatgive the largest volume of the box. What is themaximum volume of the box?

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.(a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes.(b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.(c) Write an expression for the volume V in terms of both x and y.V = x(3−2x)(3−2x) (d) Use the given information to write an equation that relates the variables x and y.y=3−2x (e) Use part (d) to write the volume as a function of only x.V(x) = x(3−2x)(3−2x) (f) Finish solving the problem by finding the largest volume that such a box can have.V = ft3

A rectangular box is designed to have a square base and an open top. The volume is to be 2916in.32916⁢in.3What is the minimum surface area that such a box can have?

Find the dimensions of the rectangular box of maximum volume that caninscribed in a sphere of radius 4.