A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters. What dimensions (height and radius) will minimize the material needed to produce each can, that is, minimize the surface area?

Q: A food manufacturer packages his product in 1-liter cans that are right circular cylinders. If the…

A:

Q: For a closed rectangular box, with a square base x by x cm and height h cm, find the dimensions…

A:

Q: Suppose we have 45 m^2 of material to build a box with a square bottom and no top. What dimensions…

A:

Q: A cylindrical container with a circular base and open top must have a volume of 1000 m³. Find the…

A:

Q: A company wants to manufacture cylindrical aluminum cans with a volume of 1000 cm3. What should be…

A:

Q: The diameter and height of a paraboloid are 1 m and 2 m respectively. Determine its dimensions when…

A: Given, Diameterd=1 mHeighth=2 m The formula for finding the volume of the paraboloid is, V=π2hr2

Q: The base of a rectangular prism shaped aquarium without a lid is made of slate and the sides are…

A: Given Volume of the tank V=96 m3 Cost of slate (S) = 3 Cost of Glass (G) (per unit area) S=3G

Q: Find the dimensions of a cylindrical can with a volume of 666 in^3 that minimizes the surface area.…

A: To find the dimensions of a cylindrical can with a volume of 666 in3 that minimizes the surface…

Q: The total surface area of an industrial cylindrical autoclave is to be limited to 20m^2. If it is…

A: Total surface area of the cylinder = 20 m2Formula for calculating the total surface area of the…

Q: You are to construct an open rectangular box from 12 ft2 of material. What dimensions will result in…

A:

Q: An open-top rectangular box is being constructed to hold a volume of 350 in. The base of the box is…

A: First derivative of a function when equated to 0 gives us the critical points of the function where…

Q: A pencil cup with a capacity of 36 in.3 is to be constructed in the shape of a rectangular box with…

A:

Q: Determine the dimensions of a rectangular box with a volume of 1 ft ^ 3 that has a minimum surface…

A: Given a rectangular box with volume 1 ft^3

Q: The Soup Company is constructing an open-top, square-based, rectangular metal tank that will have a…

A: Let dimension of tank be a*a*hBase area=a*a=a2height of tank=hgiven,   volume=32+t3   a2h=32…

Q: A box with a square base and open top must have a volume of4000 cm^3. Find the dimensions of the box…

A:

Q: A jewelry box with a square base is to be built with copper platedsides, nickel plated bottom and…

A: Given that Volume of the  box is 40 cm3 Base of the box is square. Let  length =width=x Height=y…

Q: A cylindrical can, open at the top, is to hold 200 cm³ of liquid. Find the height, h, and the…

A: Consider the given: The given volume of the cylinder is 200 cubic cm. V=πr2h200=πr2hh=200πr2 Find…

Q: Postal regulations require that for a rectangular package with a square base, the perimeter of the…

A:

Q: Determine the dimensions and surface area of a rectangular box, open  at the top, having volume V,…

A: Determine the dimensions and surface area of a rectangular box, open  at the top, having volume V,…

Q: A closed rectangular box has volume 26cm^3. What are the lengths of the edges giving the minimum…

A: Given a rectangular box which has volume 26 cm^3.

Q: You are to construct a closed rectangular box with volume 27cm^3. If the base of the box is x by x…

A:

Q: A company is constructing an open-top, square-based, rectangular metal tank that will have a volume…

A:

Q: Determine the dimensions of a rectangular box, open at the top, having volume V, and requiring the…

A: Let  Length=xWidth=yHeight=z Then volume of the box is  v=xyzz=vxy…

Q: What dimensions will maximize the lateral surface area of an inverted cone, if V = 27 cm³?

A:

Q: A Box with a Square base and an open Top must have a volume of 500 cm'. Find the dimensions of the…

A: A box with a square base and an open top must have a volume of 500 cm. To find: The dimensions of…

Q: In constructing an open rectangular box from 48 ftf of material, what dimensions will result in a…

A:

Q: You want to produce a cylindrical water container with a capacity of 350mL. What dimensions will…

A: We have to find the dimensions of the cylinder.

Q: A cylindrical can, open at the top, is to hold 600 cm³ of liquid. Find the height, h, and the…

A:

Q: To calculate: The dimension of the rectangular solid with a square base that yields the minimum…

A: The rectangular solid has a square base. Let the dimensions of the rectangular solid be x, x and y.…

Q: If a closed tin can of volume 16? in3 is to be in the form of a right-circular cylinder, find the…

A: Consider the provided question, In your question given, If a closed tin can of volume 16? in3 to be…

Q: The volume of the closed cylindrical tank is 11.3 m 3 . If the total surface area is a minimum, what…

A: Given: Volume of cylindrical tank is 11.3m3.

Q: Manufacturer X is planning to produce a closed balikbayan box as they anticipate the surge of…

A:

Q: A cylindrical can is to have a volume of 400 cubic centimeters. Find the dimensions (height and…

A:

Q: A pharmaceutical company wants to manufacture cylindrical aluminum cans with a volume of 1000 cm3 (1…

A: Since we know that, Surface area of cylinder, S=2πrh+2πr2      ...(1) And volume of cylinder, V=πr2h…

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins.  What…

A: Given volume of the can is (128)πcm3 Let height=h radius=x

Q: A box, used to package men's shirts, is in the shape of a square-based prism and its to have a…

A: Given Data: The volume of the square-based prism is: V=8400 cm3 The equation of surface area is:…

Q: An open-top rectangular box is being constructed to hold a volume of 350 in. The base of the box is…

A: Given :  an open top rectangular box is being constructed to hold a volume of 350 in3, the base of…

Q: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.…

A: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.

Q: A MANUFACTURER NEEDS TO MAKE A CYLINDRICAL CAN THAT WILL HOLD 1.5LITRES OF LIQUID . Determine the…

A: Given :  volume of the cylinder π r2h      Surface area = 2 π r h + 2 π r2 To Minimize: Surface…

Q: The cost of producing an ordinary cylindrical tin can is determined by the materials used for the…

A: Given:       Volume =1000 cm3       Volume of cylindrical tin V=πr2h      then,            πr2h=1000…

Q: A closed rectangular box with square base is to be constructed. Suppose the volume is 27 cubic cm.…

A:

Q: I will accept a package whose combined height and perimeter of the base are at most 140 inches. Use…

A:

Q: A thin-walled cone-shaped cup (see figure) is to hold 36t cm of water when full. What dimensions…

A:

Q: A rectangular box with no top is to be constructed having a 125 cubic inches. What width r, in 2…

A:

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins. What should…

A: Use application of derivative concept. volume of cylinder and total surface area of cylinder…

Q: should the box have in order to minimize the surface area?

A:

Q: Consider a right circular cylinder open top tin can with volume 1000 cm³. Suppose R and H are the…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We will use Lagranges multiplier method to find dimension of the box .