Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 441 square meters.

Q: The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the…

A: Given that volume =4000cm3 find the dimensions of the box that minimize the amount of material used…

Q: A packaging company is going to make open-topped boxes out of 20 cm by 20 cm rectangles of cardboard…

A:

Q: 4. An open-top box with a square bottom and rectangular sides is to have a volume of 256 cubic…

A:

Q: A manufacture wants to design an open box having a square base and a surface area of 256 square…

A:

Q: A rectangular box having a square base and open at the top is to have a capacity of 16,823 cubic…

A: suppose the side of the box = x cm.height= h cm.Given : Volume  = 16823 cc

Q: A rectangular tank with a square base, an open top, and a volume of 6912 ft° is to be constructed of…

A:

Q: A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle whose…

A: A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle whose…

Q: what are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic…

A: This is a problem of optimization.

Q: Find the length L and W (with W(less than or equal to) L) of the rectangle with perimeter 48 that…

A:

Q: A shipping company handles rectangular boxes provided the sum of the length, width, and height of…

A: Let the dims be x, y and z then volume V=xyz           -----------(1) and the restriction we have…

Q: A Norman Window has the shape of a rectangle surmounted by a semicircle. If a Norman window is to…

A: Given, The perimeter of the window = 28 ft  Height of rectangular part = y width of rectangular part…

Q: A rectangular prism has a height of 11.5 inches, a length of 9.6 inches, and a width of 2.10 inches.…

A:

Q: 8. Find the dimensions of the rectangular box, open at the top, which has a maximum volume if…

A: Given surface area is 18 square feet.

Q: maximum. 28. Find the dimensions of a closed rectangular box (top included) of the largest volume if…

A: Using the constrain of the surface area, we can set up the equation for the volume.The function for…

Q: A rectangular box having a square base and open at the top is to have a capacity of 16823 cc. Find…

A: Given; A rectangular box having a square base and open at the top is to have a capacity of 16823 cc.…

Q: A closed cylindrical can is to have a surface area of 8 square units. Show that the can of maximum…

A:

Q: A closed box is in the shape of a rectangular solid with height 3 m. Its surface area is 268 m2. If…

A: Consider the closed box is in the shape of rectangular solid having height 3 m. The surface area of…

Q: An open box is to be made of a piece of cardboard 10cm x 16cm by cutting equal squares out of the…

A:

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. Find the dimensions of a…

A: Given that the perimeter is fixed.Let us assume that the length of the rectangle part which is also…

Q: Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its…

A: According to the question, we have a rectangular box and the sum of the lengths of its 12 edges is…

Q: 5. FIND THE MAXIMUM AREA FOR A RECTANGULAR ENCLOSURE USING 480 FEET OF FENCING MATERIAL AND…

A: I am attaching image so that you understand each and every step.

Q: rectangular prism has demensions of 18cm by 12cm, by 24cm. If the density of the prism is .036g/cm3.…

A:

Q: An open box is to be made from a square piece of material, 12 inches, by cutting equal squares from…

A: Here we use the concept of APPLICATIONS OF DERIVATIVES

Q: Example Find the dimensions of the rectangular box with an open top with largest volume if the total…

A: Given : Total surface area of the rectangular box is 216 cm²

Q: An open box will be made by cutting a square from each corner of a 10-cm by 16-cm piece of cardboard…

A: To find: The size of square to be cut from the corner of cardboard to maximize volume and also find…

Q: Find the dimensions of the closed rectangular box of largest volume with surface area of 16 m². What…

A:

Q: A container with square base, vertical sides, and open top, is to be made from 3,000 ft² material.…

A:

Q: A cardboard box without a lid is to have a volume of 4000cm3. Find the minimum amount of cardboard…

A:

Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A:

Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

A:

Q: A square-based prism has a volume of 8000 mm3 . What are the dimensions of the prism for the minimum…

A: Consider a square-based prism which has a volume of 8000 mm3.  The objective of the problem is to…

Q: A rectangular tank with a square​ base, an open​ top, and a volume of 37,044 ft3 is to be…

A: Given,Volume of the rectangular tank = 37044 ft3

Q: An open rectangular box has an area of 441 cm2. If its length must be 3 times its width, find its…

A:

Q: A square with dimensions 12 cm, 2 cm, 9 cm and a cube have equal volumes. Calculate the edge of the…

A:

Q: A pressure tank has a hemispherical base surmounted by a right circular cylinder and which in turn…

A: we know that volume of semi sphereV1, volume of right circular coneV2 and volume of cylinder V3 is…

Q: A tube of lip balm has a height of 2.75 inches and a diameter of 0.75inches.  a. if the cap on the…

A: Part (a):Diameter of the lip balm tube, d = 0.75 inches. Thus, the radius of the tube is r = d/2 =…

Q: A rectangular solid with a square base has surface area 337.5 square centimeters.  V =…

A:

Q: Phil wants to design an open box with a square base with a surface area of 400 square inches. What…

A: We need to find dimensions of a box whose volume is maximum.  & volume = x^2 y

Q: An open box is to be made from a square piece of material, 12 inches by 12 inches, by cutting equal…

A:

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: Given: The total perimeter is 16 feet. The given window is formed by adjoining semicircle to the top…

Q: A rectangular page contains 65 cm? of print. The top and bottom margins of the page are each 0.5 cm…

A:

Q: A box with a square base and with height f(x) is to be constructed so that it has a volume of 1000…

A: A box with a square base.  Let the side of the base be x cm. x>0 If the height of the box is…

Q: a rectangular tank that is 864 ft cubed with a square base and open top is to be constructed of…

A: Let the measure of side of square base of tank  is x ft and height of tank is y ft and volume of…

Q: Q17 A box with a square base with side length b and height h and with an open top must have a volume…

A: We have to find the dimensions of the given box.

Q: An open box is to be made from a square piece of material by cutting equal squares from each corner…

A:

Q: The surface area of an open-top cylindrical box is 27π cm ². Determine the dimensions of the…

A:

Q: Find the dimensions of a rectangle with area 1728 m whose perimeter is as small as possible. (I both

A: Length of rectangle = 24√3 m  Width = 24√3 m

Q: A rectangular tank with a square base, an open top, and a volume of 16,384 ft° is to be constructed…

A: Given : Volume of rectangular is given 16384 ft3  Now we find surface Area and dimensions

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.