A storage unit has the shape of a hemisphere on top of a cylinder and a fixed volume V (Figure 10a). Determine the dimensions of the solid (the radius R and the height H) that minimize the total surface area.

Q: Suppose that r = 12 cm and h = 15 cm in the right circular cylinder. Find the exact and approximate…

A: In right circular cylinder   radius(r)=12 cm and height(h)=15 cm (a)  For lateral surface area…

Q: If the area bounded by y = x² and y = 2 – x² is revolved about the x – axis and a vertical…

A: We have to find the volume of the solid if the area bounded by y=x2 and y=2-x2 is revolved about the…

Q: 14. Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

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Q: Given an area D bounded by curve y = 4x−x^2, line x+y = 6, and y-axis. Find the volume if the area D…

A: We are given an area D bounded by curve y = 4x - x2, line x + y = 6, and y-axis. We need to find the…

Q: The diameter and height of a paraboloid are 1 m and 2 m respectively. Determine its dimensions when…

A: Given, Diameterd=1 mHeighth=2 m The formula for finding the volume of the paraboloid is, V=π2hr2

Q: Rotate a circle of radius r around the x axis and use the method of disks to prove the formula for…

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Q: Find the volume of the solid that results when the region enclosed by y = Vx, y = 0, and x = 9 is…

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Q: Find the volume generated by the area bounded by the parabola x=√ay , and the line y=b that is…

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Q: Find the radius and height of a cylindrical can of total surface area A whose volume is as large as…

A: Find the radius and height of a cylindrical can of total surface area A whose volume is as large as…

Q: 2. The area of the parabola x2 = 4y – 4 cut through its latus rectum is revolved about the…

A: 2) Parabola; x2=4y-4End points of the latus rectum (-2,2) and (2,2)vertem = (σ 1)using washer method

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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Q: What is the volume, br^3, of the rotating body obtained by rotating the graph of the function y = Vx…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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Q: A sphere has a radius of 5.81 in., with a possible error of ± 0.003 in. Estimate the maximum error…

A: For a sphere of radius r the expression for the volume is V=43πr3. The error in r is denoted as ∆r.…

Q: Find the volume of the solid formed by rotating the region enclosed by eA# + 5, y = 0, x = 0, x =…

A: olume by shell method is given below

Q: For a right circular cylinder, suppose that r = 6 in and H - 7 in. Find the exact:Total area,…

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Q: Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the…

A: The volume of a solid formed by revolving the region bounded by the curve y=f(x) and the x axis is…

Q: . THe area enclased by the loop of the curved y= x (x - 3)° is Find the volume generated . revolved…

A: Here 1st we will find points where loop is formed and then shade the region bounded ,  To form the…

Q: Find the volume of the solid whose base is the semicircle y = /25 – x² where –5 < x < 5 and the…

A: Given the base of the solidy=25-x2 , y&gt;0The intersection of the base with the x-axis :Put y =…

Q: Find the volume of the tetrahedron bounded by 2x−y+z = 4 and the coordinate planes.

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Q: If the region enclosed by the y-axis, the line y=2 and the curve y=sqrtx is revolved about the…

A: Proceed as shown below...

Q: The area in the second quadrant of the circle x2 + y2= 2 is revolved about the line y + 1 = 0. What…

A: This problem belong to circle and line section from geometry and we solve this using the second…

Q: Find the volume limited by the graphs of the equations

A: Part (a):

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^2, y=1,…

A: We will integrate cross sectional area of any x to get the volume of solid.

Q: Given that the altitude is 2/3 of the total altitude of a cone which is 10m and the base of the cone…

A: The volume of the frustum can be obtained using the formula V=13πH(R2+Rr+r2). Here, H is the height…

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

A: Base of the tank is square based so let length = breadth = x let height = y Volume = length ×breadth…

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

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Q: Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z…

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Q: Show by integration that the volume of a sphere of radius r is V=4/3 πr³

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Q: Find the volume of the solid whose base is the region enclosed by y=x^2 and y=4, and the cross…

A: Given: Region enclosed by y=x^2 and y=4. And the cross sections perpendicular to the y-axis are…

Q: Derive the formula for the volume of a sphere of radius r.

A: The volume of cylindrical element with radius x and altitude dy.                    dV  =  πx2 dy…

Q: The base of a solid is in the first quadrant bounded above by y = 5 and below by y = √5x between x =…

A: The given curves are y=5, y=5x, x=0, x=5 which forms the base of a solid. The cross section of the…

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 9 and whose cross…

A: To find the volume of the solid whose base is bounded by the given circle and whose cross-sections…

Q: Show that (a) the total surface of the cube is twice the square of its diagonal, fo) the volume of…

A: Given- A cube with side s. To show- That Show that (a) the total surface of the cube is twice the…

Q: The volume of the closed cylindrical tank is 11.3 m 3 . If the total surface area is a minimum, what…

A: Given: Volume of cylindrical tank is 11.3m3.

Q: What is the volume of the solid whose base is the interior of the parabola y2 = x from x=0 to x=4…

A: Given parabola equation is  y2=xTake square root on both sidesy=x Now we find area of square shaped…

Q: Show that the rectangular box (including the top and bottom) withfixed volume V = 27 m3 and smallest…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: For a cylindrical can (depicted in the figure, height h and radius r) with volume 2π m³, compute the…

A: Surface area = 2πrh+2πr2 Volume =πr2h = 2π

Q: A sphere has a volume of V= 2916 in. Find its surface area.

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Q: a truncated hexagonal right prism has an average lateral edge of 24cm. what is the volume of the…

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Q: The volume of a right circular cone is 36 t. If its altitude is 3, find its radius.

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Q: If the area bounded by the parabola y = x² and the line y = x is revolved about the x – axis, the…

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

A:

Q: The base of a solid is bounded by the graph of x² + y² = a², where a > 0. Find the volume of the…

A: The base of the solid is the disk x2+y2≤a2, where a is the radius as shown below: The boundary…

Q: Find the mass of a circular cone of height b and radius of base a whose density varies as the…

A: To find: The mass of a circular cone. Given information: The height of the cone is b and base is a…

Q: Given the area in the first quadrant bounded by x²=8y, the line y-2=0 and the y-axis, what is the…

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Q: Find the dimensions of the open cylindrical tank where the volume inside is maximized and that the…

A: Let r, h  be the radius of the cylindrical tank. Now, Let S represent the  Surface area  of the open…

Q: Find the volume of the solid whose base is the semicircle y = v9 – x2 where -3 < x < 3, and the…

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