4. West Coast Customs is constructing and open-top, square-based, rect- angular subwoofer box that will have a volume of 64 ft³. What dimensions minimize the surface area? What is the minimum surface area?.

Q: 3. Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We need to find dimension of an open box that maximizes the volume.

Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1300 cm2 and whose…

A:

Q: 7. A manufacture want to design an open box having a square base and a volume of 256 cm³. What…

A: Given problem is :

Q: Your ironworks made an agreement to build a 500ft² volumed, square based, hypaethral, rectangular…

A: The tank is square based and rectangular. Let the length of the base be x  let the height of the…

Q: 4. A manufacturer wants to design an open box having a square base and a surface area of 1200 cm2.…

A: Given:  A manufacturer wants to design an open box having a square base and a surface area of 1200…

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

A:

Q: Find the dimensions of a box with largest volume whose surface area is 100 cm?. Lagrange multipliers

A:

Q: 6. Find the minimum surface area of a box that holds 2 cubic meters.

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: What is the largest possible area such a region can have if its perimeter is to be 20 units?

A:

Q: Determine the dimensions of the inscribed rectangle of maximum area. y = e¯*

A: Let the point on the curve for the rectangle with maximum area is (x,y) It can be written as: so…

Q: 2. Calculate the volume of a water cylinder with total height of 10 meters and whose diameter is 400…

A: Given:height=10mDiameter=400 cmVolume of a cylinder=2πrh1m =100 cm

Q: If the dairy uses a rectangle container opti dimensions and the surface area be?

A: Given a dairy sells ice cream in 11.4 L cardboard container.

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 rectangular storage container with a square base and an open top is to have a fixed volume of…

A:

Q: Find the exact maximum and minimum volumes (in cm) of a rectangular box whose surface area is 1,300…

A:

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

A:

Q: 6. Marcus is constructing a rectangular pricm using exactly 96 cm² of cardboard. will have the…

A:

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

A:

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

A: Let x and y be the base and height of the rectangular metal tank.  Given, volume = 36 ft3 Find the…

Q: 1. The volume of the closed cylindrical tank is 11.3 m³. If the total surface area is a minimum,…

A: Surface area and Volume of a cylinder: The amount of space covered by the flat surface of the…

Q: West Coast Customs is constructing a closed-top, square-based, rect- angular subwoofer box that will…

A: Here we use application of derivatives to find the minimum surface area and find it's dimensions.

Q: A cylinder with no top is to have a volume of 100π cubic centimeters. Find the minimum possible…

A: To find the minimum possible surface area of the given type of cylinder.

Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

A: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

Q: 4.) Find the minimum amount of tin sheet in square inches that can be made into a closed cylinder…

A: The given question can be solved as shown in step2

Q: what is the minimum perimeter that a rectangle with an area of 32 ft2 can have?

A:

Q: 11. A telephone booth in the shape of a square-based prism is to have a volume of 832 m³. Determine…

A:

Q: 7. Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

A: Given :Volume = 32 ft3

Q: 1. Find the dimensions of a rectangular box with a square base and no top that has a volume of 100…

A: Solve By minimizing surface area

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: 7. Determine the dimensions of a rectangular box, open at the top, havin volume of 32 ft3, and…

A: Given that the volume of the rectangular box is 32 ft3.

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

A:

Q: A rectangular tank with a square base, an open top, and a volume of 8788 ft 3 is to be constructed…

A: A rectangular tank has square base Let x be the base of the tank  and y be the height  x is the…

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

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

Q: A box with a square base and open top must have a volume of 13,500 cm3. Find the dimensions of the…

A: Topic = Volume

Q: The volume of a closed cylinder tank is 11.3 m3 . If the total surface area is a minimum ,what is…

A: Introduction :

Q: Find the dimensions of a rectangle with area 100 m? whose perimeter is as small as possible? Find…

A: to find:- dimensions of the rectangle. minimum perimeter.

Q: The volume of the closed cylindrical tank is 11.3 m³. If the total surface area is a minimum, what…

A: In this question, concept of volume and surface area of cylinder is used. Volume and Surface area of…

Q: Determine the dimensions of the inscribed rectangle of maximum area.

A: Determine the dimensions of the inscribed rectangle of maximumarea.

Q: 4. Find the maximum area of an isosceles triangle inscribed in a circle of radius r.

A:

Q: A box with a square base and open top must have a volume of 2500 cm3. What is the minimum possible…

A: Let's assume the sides of the square base = a and height of the box = h  So, the volume of the box =…

Q: A triangular prism has a base which is an isosceles right triangle. If the volume of the prism is…

A:

Q: 3. If find the largest possible volume for the box. 1200cm of material is available to make a box…

A: We can find the answer as below.

Q: Mayor John proposed to utilize a government-owned land with an area of 12, 150 m2. One-third of the…

A: This is a application of derivative problem

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

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 .