A company plans to manufacture a rectangular container with a square base, an open top, and a volume of 2,916 in3. Determine the dimensions of the container that will minimize the surface area. What is the minimum surface area? Enter only the minimum surface area, and do not include units in your answer.

A company plans to manufacture a rectangular container with a square base, an open top, and a volume of 2,916 in3. Determine the dimensions of the container that will minimize the surface area. What is the minimum surface area? Enter only the minimum surface area, and do not include units in your answer.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.4: Polyhedrons And Spheres

Problem 28E: Given that a regular polyhedron of n faces is inscribed in a sphere of radius length 6 in., find the...

See similar textbooks

Similar questions

A rectangle has an area of 36 in2. What is the limit smallest possible value of the perimeter of the rectangle?
Given that a regular polyhedron of n faces is inscribed in a sphere of radius length 6 in., find the maximum largest possible volume for the polyhedron.
West Coast Customs is constructing a closed-top, square-based, rectangular subwoofer box that will have a volume of 32ft^(3). What dimensions minimize the surface area? What is the minimum surface area?.
what is the minimum possoble perimeter for a rectangle whose area is 100 in^2
A box (which includes all 6 sides) is being constructed with a rectangular base. The base has length 3 times itswidth. If the box must hold a volume of 200 cubic centimeters, what is the minimum possible value for its total surfacearea?
A rectangular prism has a height of 11.5 inches, a length of 9.6 inches, and a width of 2.10 inches. The volume is 232 inches and the surface area is 317.4 inches. Through optimization, what would be the minimal surface area?
A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 108 cm3. Determine the dimensions of the box that will minimize the surface area. What is the minimum surface area? Enter only the minimum surface area.
Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 180 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions?
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
A box with a square base and an open-top is to be constructed. The base will be made of material costing $3 per square foot, and the sides will be made of material costing $1 per square foot. What is the minimum cost to construct a box with a volume of 324 cubic feet?
A rectangular tank with a square base, an open top, and a volume of 8788 ft 3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.