21. Optimization A right triangle has legs of length h and r, and a hypotenuse of length 4 (see figure). It is revolved about the leg of length h to sweep out a right circular cone. What values of h and r maximize the volume of the cone? (Volume of a cone = ar'h/3.) h

Q: A box with a square base and open top must have a volume of 500 cm3cm3. We wish to find the…

A: The length of the base is x and the height is h. Since the base is a square, the surface area of…

Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

A:

Q: Consider a wire of length 7 ft. The wire is to be cut into two pieces of length z and 7 - 1. Suppose…

A: We have wire of length 7 ft. The wire is to cut into two pieces of length x and 7-x.Here the length…

Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

A: Let, two sides= x and another side= y So, 2x+y=12  y=12-2x

Q: (b) An open box with a square base and a surface area of 2700 square inches is needed. Find the…

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Q: Optimal garden A rectangular flower garden with an area of30 m2 is surrounded by a grass border 1 m…

A: Consider the length of the flower is L and width is W. Then To minimize the combined area of garden…

Q: A rancher is building a horse pen on the corner of her property using 1000 ft of fencing. Because of…

A: Given: A rancher is building a horse pen on the corner of her property using 1000 ft of fencing.…

Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

A: We have to find largest valume that a such box hve.

Q: 3) What are the dimensions of a right circular cylindrical can that will hold a volume of 512 cubic…

A: Dimensions of right circular cylinder

Q: You need to construct a cylindrical container with a circular base and no top, having a total…

A:

Q: 31. Cost In redecorating an office, the cost for new carpeting is $40 per square meter and the cost…

A: Concept: The Lagrange multiplier method: The Lagrange multiplier method is a method for determining…

Q: 20. Minimizing surface area. Drum Tight Containers is designing an open-top, square-based,…

A: Volume of a cuboid is lbh. Since it is mentioned that it is square-based so l=b. l2h=62.5 in3…

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

A: volume of can = πR2H=1000  ⇒H=1000πR2   ...(1)surface area A=πR2+2πRH=πR2+2πR1000πR2=πR2+2000R

Q: 55. A cardboard box without a lid is to have a volume of 32,000 cm³. Find the dimensions that…

A:

Q: 24) you are designing a rectangular poster continue to contain 27 in.² of printing with a 3 inch…

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Q: A square plate with sides of unit length has its center at the origin of an x-y coordinate plane;…

A: Given :  A square plate with sides of unit length has its center at the origin of an x-y coordinate…

Q: The volume of a cylinder is 900 cubic cm. Find the dimensions in cm that will minimize the surface…

A: The volume of a cylinder is 900 cm3

Q: A covered box is to be made from a rectangular sheet of cardboard measuring 10 inches by 16 inches.…

A: Volume of the box=x.y.z —1                                   height*lenth*width    2x+z=10  —2…

Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

A:

Q: A cardboard box without a lid is to have a volume of 16,384 cm³. Find the dimensions that minimize…

A: Volume of the cardboard =16,384 cubic cm let x= length of side of the box, h= height of the box y=…

Q: A piece of wire 29 m long is cut into two pieces. One piece is bent into a square and the other is…

A: A piece of wire 29 m long is cut into two pieces. One piece is bent into a square and the other is…

Q: 2) The diagram shows a square with cross-section x units by x units, and 9- 2x units. Find maximum…

A: From the given diagram; The expression for the volume of the given prism is:…

Q: A school is building a 1 km race track. The school wants the track to be as big as possible. What…

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Q: A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material…

A:

Q: You have been asked to design a rectangular box with a square base and an open top. The volume of…

A: See this solution in below

Q: 5. A tank is to be constructed of some fixed volume V . The tank is built by placing two hemispheres…

A: The total volume of the tank will be,

Q: 14. A box with a square base and open top must have a volume of 32,000 cm³. Find the dimensions of…

A:

Q: 10. You have a load of tiles that can cover an area of 400 t. You want to cover a rectangular shape…

A: From the given equations  P=2x+2(400/x) P=2x+(800/x) P'(x)=2-(800/x2)=0 x=20

Q: A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The material…

A: Given A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The…

Q: 1. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

A: The solution is given in the next steps.

Q: A manufacturer needs to make a cylindrical can that will hold 1500 cubic centimeters of liquid.…

A:

Q: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

A: Volume of the cylinder = 600 cubic centimetres. Cost of material on the side of the can = 0.03 cents…

Q: 6. Eva wants to fence two rectangular plots of land. Both plots must have the same dimensions and…

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Q: Find the volume and the dimensions of the largest rectangular box in the first octant with three…

A:

Q: 17. A Norman window is a rectangle with a semi-circle on top. If the perimeter of the window is 24…

A:

Q: 2. A 27-in gutter is bent on two sides as shown. Find the r and o values that will maximize the area…

A: From the given diagram:The cross-sectional area…

Q: 4.6 optimization #34 a closed box with a square base is to be built to house an ant colony. the…

A: Let x and y be the length of the square base of the box and the height of the box,…

Q: A piece of wire 21 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: 2 7. A soup can of volume 700 cm³ is to be constructed. The material for the top costs 0.7cents/cm²…

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

Q: Find the volume and the dimensions of the largest rectangular box in the first octant with three f…

A:

Q: 2) Elizabeth is fed up with AJ's jokes and decides to make him wear a dunce cap in calculus class.…

A: Cone is a 3-D shape that tapers smoothly from a flat base to a point called the apex or vertex.

Q: A cardboard box without a lid is to have a volume of 27,436 cm3. Find the dimensions that minimize…

A: Given: A cardboard box without a lid is to have a volume of 27,436 cm3 To determine: The dimensions…

Q: 12. A rectangular box with a square base and an open top must have a volume of 500 cm. The box…

A:

Q: A cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material…

A: Given that cylinder can hold 250 cubic centimeter of soup so  Volume of cylinder…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400…

A: Let r and h (in cm) be the radius of base and height of the cylindrical package respectively. Volume…

Q: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

A:

Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

A: Note: There are multiple sub-questions. No specific question has been asked. So, We will solve the…

Q: Please help. Thank you!

A: According to the given information, a pentagon is formed by adding two sides of same length to…

Q: A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material…

A: V=450 cm3πr2h=450h=450πr2 ....(1)C(r)= Area of the sides*(rate of sides)+Area of the…