The prism has a dimension of (x+1) meters, (x+5) meters and (x+3) meters respectively. If the volume of the prism is 315m^3. What are the dimensions?
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- Find the rectangular box of maximum volume if the sum of the lengthsof the edges is 300 cm.A 2-inch square is cut from each corner of a rectangular piece of cardboard whose length exceeds the width by 4 inches. The sides are then turned up to form an open box. If the volume of the box is 64 cubic inches, find the dimensions of the box.A rectangular piece of cardboard, whose area is 143 square centimeters, is made into an open box by cutting a 2 centimeters square from each corner and turning up the sides. If the box is to have a volume of 126 cubic centimeters, what size cardboard should you start with?
- A 120-m long fence is to be cut into pieces to make three enclosures, each of which is square. How should the fence be cut up in order to minimize the total area enclosed by the fence?A box is being constructed by cutting 4-inch squares from the corners of a rectangular sheet of metal that is 10 inches longer than it is wide. If the box is to have a volume of 476 cubic inches , find the dimensions of the metal sheet.Find the area(square meters) of the largest rectangle that can be inscribed in an equilateral triangle of side 2 meters if one side of the rectangle lies on the base of the triangle.
- Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius 7.Find the volume of the largest box that can be made by cutting equal squares out of the corners of a piece of cardboard of dimensions 15 inches by 24 inches and then turning up the sides.A rectangular piece of cardboard, whose area is 198 square centimeters, is made into an open box by cutting a 2-centimeter square from each corner and turning up the sides. If the box is to have a volume of 196 cubic centimeters, what size cardboard should you start with?
- An open box is to be constructed from a square piece of sheet metal by removing a square of side 4 feet from each corner and turning up the edges. If the box is to hold 256 cubic feet, what should be the dimensions of the sheet metal?According to postal regulations, a carton is classified as “oversized” if the sum of its height and girth (perimeter of its base) exceeds 108 in. Find the dimensions of a carton with a square base that is not oversized and has maximum volume.Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 168in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions?