A rectangular beam will be cut from a cylindrical log of radius 10 inches. Suppose that the strength of a rectangular beam is equal to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.

Q: A rectangle is to be inscribed in a semicircle of radius 2. What is the largest area the rectangle…

A:

Q: steel girder 27 ft long is to be moved on a rollers along a passageway 8ft inches wide and into a…

A: We have to find a relative extremum for the width of the corridor (y) such that the girder can touch…

Q: An open rectangular box with square ends to hold 6400 cu ft, is to be built at a cost of $75 per sq…

A: Given that, An open rectangular box with square ends to hold 6400 cu ft. Thus, V= x2 y. 6400 = x2y…

Q: A 100 cm piece of wire is going to be cut in two pieces. One will be bent into a square, and the…

A:

Q: Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. Show…

A: Given:Perimeter of a rectangle is 68 m.

Q: Suppose a long rectangular sheet of metal, 16 inches wide and 12 feet long, is to be made into a…

A: 12feet= 144 inch. width=16 inches. length=144 inch. Let x width turned both sides. so ,volume of the…

Q: An open rectangular box with square ends to hold 6400 cu ft., is to be built at a cost of $0.75 per…

A: The rectangular box is square at base and opened at top.So we will not be involving top of the box…

Q: . The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

A:

Q: A rectangle has a length which is twice that of its width. Also, it's area is twice that of its…

A: This question is related to area and perimeter of rectangle, we will solve it using the given…

Q: An open box with a volume of 128 cm³ can be made by cutting a square of the same size from each…

A:

Q: A semi-elliptical goblet has a depth of 4 inches and its round opening has a width of 3 inches. It…

A:

Q: The cabinet that will enclose the Acrosonic model D loudspeaker system will be rectangular and will…

A: Given- The cabinet that will enclose the Acrosonic model D loudspeaker system will be rectangular…

Q: According to postal regulations, a carton is classified as “oversized” if the sum of its height and…

A: Assume a be the side length of the square base,h be the height of the carton and V be the volume of…

Q: The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area…

A: Maxima and minima problem

Q: A truck has to pass under an overhead parabolic arch bridge which has a span of 20 meters and is 16…

A: Given,           A truck has to pass under an overhead parabolic arc bridge which has a span of 20…

Q: An open box is to be made from a 6 ft by 16 ft reetangulas card board by cutting out equaL squares…

A:

Q: If the diameter of the base remains constant, by what factor should the altitude be multiplied to…

A:

Q: A window is in the form of an equilateral triangle surmounted on a rectangle. The rectangle is of…

A:

Q: The cabinet that will enclose the Acrosonic model D loudspeaker system will be rectangular and will…

A:

Q: Suppose a rectangular picture frame has a thin border made from a 144-inch-long strip of bronze. If…

A: # Considering the width of border negligible Length of the strip is 144 inch Now let the length of…

Q: 2, i, Find out the roots of the following by completing the square. 5x^2-2x-4-0 ii, Calculate the…

A:

Q: If the length of three sides of a trapezium other than base are equal to 10 cm, then find the area…

A:

Q: Suppose that the radius and height of a cylinder must add to be 15 cm. What radius and height will…

A:

Q: A rectangular field is four times as long as it is wide. If the perimeter of the field is 500 yards,…

A:

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

A: Let x be the width and y be the length of the rectangle.From the given statement, the three side…

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

A: Given  Total length of the fence=2500 m Letl=length of the plotb=width of the plot

Q: Find the dimensions of the right circular cylinder of greatest volum that can be inscribed in a…

A: Given query is to find the dimensions of a right circular cylinder that can be fit inside a sphere…

Q: A rectangle has a length 2 m less than twice its width. When 2 m are added to the​ width, the…

A:

Q: Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral…

A:

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

A: Given length of wire is 700 m. rectangular plot's three sides are bounded by electric fence.

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

A:

Q: A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides…

A:

Q: If 1200 cm² of material is used to make a closed cardboard box with a square base. Find the exact…

A: This question can be solved using the concept of maxima and minima.

Q: The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

A:

Q: Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

A: Let x and y be the length and width of the rectangle inscribe in a circle of radius a. Then the…

Q: A rectangular field is three times as long as it is wide. If the perimeter of the field is 400…

A: Suppose that the width of a rectangular field is x then the length of the rectangular field is 3x.

Q: The front face of a tent is triangular and the height of the triangle is two-thirds of the base. The…

A: Let us assume that the base of the front face= x So the height = 2x3 Length = x+3  Given volume =…

Q: If the length of three sides of a trapezium other than the base are equal to 10cm, then find the…

A:

Q: A rectangular box is to be made from a square piece of cardboard of side length 10 inches by cutting…

A: We need to determine dimension of box.

Q: The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

A: Given :             Cube side a = 6 feet Error in side :                       ∆a = 1.5 inches∆a =…

Q: A conical water tank with vertex down has a radius of 13 feet at the top and is 30 feet high. If…

A: Given,            A conical water tank with vertex down has a radius of 13 feet at the top and is 30…

Q: A cylindrical tank with length 5 ft and radius 3 ft is sit- uated with its axis horizontal. If a…

A:

Q: A 3" x 5" picture is to be enlarged such that its new length is five times the width of the original…

A: A 3" x 5" picture is to be enlarged such that its new length is five times the width of the original…

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

A: Let a and b be the sides of a retangular fence.

Q: Find the values for each of the dimensions of an open-top box of length x, width y, and height…

A:

Q: 2. The area of a rectangular field is 162 sq. m and its length is twice its width. Find the…

A: Given,            Area of the rectangular field is 162 sq. m

Q: When a bullet is fired into a sand bank, its retardation is assumed equal to the square root of its…

A: Given is the retardation equal to square root of velocity. WE need to find time t it will take to…

Q: A rectangular beam will be cut from a cylindrical log of radius 10 inches. Suppose that the strength…

A: Solve the given problem