should the box have in order to minimize the surface area?

Q: Find the between the porabolas area 2. X+2 メ+ 2.

A:

Q: An ice cream cone has a height of 13.5 inches and a diameter of 2 inches. What is the minimal…

A:

Q: Find the dimensions of the isosceles triangle of least area that circumscribes a circle of radius r.

A: We have given isosceles triangle that circumscribes a circle of radius 'r'.

Q: What is the area of the triangle formed if it bounded by the x and y axes and the line,  2x - 3y =9?

A: Here we have to find the area of the traingle since Area of  Triangle = 1/2 *(hight)*base

Q: Show that a rectangular box of given volume and minimum surface area is a cube.

A:

Q: How can I calculate the cross-sectional area of ​​a cone with vertex up?

A: Vertical Cross section of right circular cone is circle. Area of the circle is π (radius)2 Let the…

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

A: Consider a rectangle, inscribed in a circle of radius r.Then,

Q: If the lateral surface area of a triangular prism is 250 square centimeter with a 15 cm base length…

A:

Q: what is the lateral edge opf acube with a surface area of 294

A: Given the surface area of a cube is 294 . To find the lateral edge of a cube .

Q: Find the area of the regions enclosed by the two curves, y =x +3 and y = 4x+8. %3D

A: From the given problem:   y=x2+3 & y=4x+8       Now finding a point of intersection:…

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

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Q: Show that the rectangular parallelepiped with fixed surface area and maximum volume is a cube.

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Q: What is the area of the region bounded by the y axis with lines?

A:

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 flexible tube of length 4 m is bent into an L-shape. Where shouldthe bend be made to minimize the…

A: A flexible tube of length 4m is bent into an L-shape. Let x,y be the length of sides of L-shape.…

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: Find area enclosed by curves y=2x, y=4x^2

A: Area enclosed by two curves is the measure of the area occupied by their intersection.

Q: What dimensions will maximize the lateral surface area of an inverted cone, if V = 27 cm³?

A:

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: 3 and y=X %3D 2

A: The equation of the curve is x=12y2-3 The equation of the curve is y=x-1

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: A cylindrical can has a volume of 1024r cm. What dimensions yield the minimum surface area?

A:

Q: Find the area of the largest rectangle that can be inscribed in asemicircle of radius r

A:

Q: A closed rectangular box has volume 20 cm³. What are the lengths of the edges giving the minimum…

A: Solution is given below:

Q: How accurately should you measure the edge of a cube to be reasonably sure of calculating the cube’s…

A: The error should not be more than 2%.

Q: Find the area of a trapezoid with an altitude of length 4.2 m and a median of length 6.5 m.

A: Formula use: Area of a trapezoid whose altitude has length h and median has length m is A=hm.

Q: A cylindrical can is to have a volume of 400 cubic centimeters. Find the dimensions (height and…

A:

Q: What is the area of the decagon?

A: Given, A  regular decagon, Perpendicular distance from center to  the side of the decagon is 12.3 in…

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins.  What…

A: Given volume of the can is (128)πcm3 Let height=h radius=x

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

A: Given information: V=64 m3

Q: A Normal window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the…

A:

Q: The size of the rectangle that can be made from 200 cm long wire so that the area is maximum is ….

A: We have to find the maximum area of given rectangle.

Q: Calculate the area of ​​the region enclosed by the parabolas  y=x2 and y=2x−x2.

A:

Q: Calculate the area described by the equation y= -6x² +24x + 10, bounded by the lines x = 0 and x =…

A:

Q: A closed rectangular box with square base is to be constructed. Suppose the volume is 27 cubic cm.…

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Q: What is the area of the region bounded by the parabola y = x^2 and the line y = x?

A:

Q: A box with square base and open top has a volume of 1000 m³. Find the dimensions of the box which…

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

Q: Among all closed rectangular boxes of volume 27 cm3, what is the smallest surface area?

A:

Q: Is the rectangle of fixed area whose perimeter is a minimum a square?

A: Given Area of a rectangle =  square units-----(1)   Let length of the rectangle be feet and the…

Q: What is the perimeter of XYZ?

A: Given figure is

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

A:

Q: Suppose we want to build a cylinder that has a volume of 100 cubic centimeters. Find the radius and…

A: We have volume as constant, so we can find relation between the radius and height and use that…

Q: A box with a square base and no top has a volume of 500 cubic inches. Find the smallest possible…

A:

Q: What is the volume of a sphere whose radius is 12.0?

A:

Q: 4. West Coast Customs is constructing and open-top, square-based, rect- angular subwoofer box that…

A: West Coast Customs is constructing and open-top, square-based.rectangular subwoofer box that will…

Q: Use rectangles to estimate the area under the parabola y = x2  from 0 to 1

A: