Solid Mensuration: Prismatoid The altitude of the storage bin shown in the sketch is 12ft. and the bases.are parallel rectangles having dimensions indicated. Find the capacity.

Q: The solid obtained by rotating y = Vx,1<y<2 about the y-axis

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Q: 3) Find the Centroid of the upper half of a solid sphere of radius 1. Show all steps, but feel free…

A: The centroid of a hemisphere can also be called as centre of mass. This can be calculated by using…

Q: 1. Volume of a hemisphere Derive the formula V = (2/3)™R³ for the volume of a hemisphere of radius R…

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Q: A cylindrical pop can holds 400 cm³ of pop. How should it be constructed so that minimum amount of…

A: Here the volume of the cylindrical pop is given, that means volume is fixed as 400cm³.  Minimum…

Q: A solid lies between planes perpendicular to the y-axis at y = 0 and y=2. The cross-sections…

A: A solid lies between planes perpendicular the the y‐axis at y=0 and y=2. The cross‐sections…

Q: The plane region is revolved completely about the y-axis to sweep out a solid of revolution.…

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Q: 37. Nature uses spheres, such as oranges and grapefruits, to "package" juices. How does the surface…

A: Nature uses spheres, such as oranges and grapefruits, to package" juices.   We have to tell how…

Q: the base of a solid is the region in the first quadrant bounded by the y-axis, the x-acis, the graph…

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Q: The base of a solid is the region R in the first quadrant enclosed by the parabola y=x² +2, the line…

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Q: LA disk method is used when the solid is hollow. II. A volume can be solved using washer or disk…

A: Option II) A volume can be solved using washer or disk method.                 III) The strip using…

Q: a. Find the area of the region. Exact answers or rounded to the 3rd decimal place. b. Find the…

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Q: Establish an Intergral Por finding the surface area of the Object obtained by rotating y-'t4i16 *<5…

A: Given that  y=x^3+4 1≤x≤5  To find the surface area of the region bounds by about x axis and y axis

Q: The plane x=3 cuts the sphere x2 + y2 + z2 =25 What shape does their intersection make? Find a…

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Q: A rectangle has dimensions of 7 in. by S in. Consider the solid of revolution formed when the…

A: Given a rectangle has dimensions 7 in by 5 in. when this rectangle is revolved about the 7 in side.…

Q: Find the volume of the solid with the base is the region enclosed by the parabola y = 1– x² and the…

A: Here, the cross-sections to the x-axis are square. So, the side of the square is 1-x2. And, the area…

Q: Compare and contrast finding the volume of a solid of revolution by the disk and the shell method.…

A: The disk method is typically easier when evaluating revolutions around the x-axis, whereas the shell…

Q: 2 7 8 10 I -2 -3- The graph above shows the base of an object. Compute the exact value (in terms of…

A: Consider the region above x-axis and obtain the functions: The functions are fx=13x 0≤x≤6 and gx=2…

Q: A barrel is shaped like an ellipsoid with equal pieces cut from the ends by planes perpendicular to…

A: Given a barrel of height 2h and radius at center R and at the has radius r. To find a formula for…

Q: Find the area of the surface. The portion of the sphere x2 + y2 + z2 = 400 inside the cylinder x2 +…

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Q: Find the volume of the solid produced by rotating this two-dimensional shape using the axis shown.…

A: Given: The two dimensional figure as To find: The volume of solid produced by rotating this…

Q: the surface of the entire bead. at the right. Find the area of 3 mm. 17. A triangular prism has base…

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Q: A tank is full of water. Find the work required to pump the water out of the spot. Use the fact that…

A: Consider the given data about tank that is full of water:

Q: Carefully derive a formula for the length of a curve y = f(x) between x = a and x = b. Using this…

A: To derive a formula for finding the length of the curve y=fx between points a,b

Q: The base of a solid is a cirde with radius 5. The crous sections of the solid perpendicular to a…

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Q: Designing a gondola The designer of a 30-ft-diameter spherical hot air balloon wants to suspend the…

A: Given information:

Q: a. Find the volume of the solid obtained by rotating the region bounded by y = x³,y = 8 and x = 0…

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Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y…

A: We have to solve above given graph for volume.

Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y e*,…

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Q: erustion for the tangena plare to the Surface = 12 at the point L-2,1,3) Find an Siven by x2y2z

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Q: The base of a solid is the region enclosed by the curves : y = /¤Inx, y = 0 , x = e whose…

A: The given problem is to sketch the region bounded by curves and find the cross sectional area and…

Q: the upright area of any geometrical solid. a. lateral area b. base area c. surface area d. total…

A: Upright area of a given geometrical solid is called Surface Area.

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 500…

A: All areas are in square centimeter; volumes are in cubic centimeters and costs are in cents.

Q: the moment of inertia of the area bounded by the cubic parabola a^2 y = x3, the y – axis and the…

A: To find the moment of inertia of the area bounded by the below equations about the y-axis.…

Q: Find the volume of the solid generated by revolving the region enclosed by the triangle with…

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Q: calc 3 Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 81, above the…

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Q: We model pumping from spherical containers the way we do from other containers, with the axis of…

A: Let us cut a slice of water of width ∆y, -y mfrom the top. so the radius of the slice r=49-y2

Q: Find the volume of the described solid. 23) The solid lies between planes perpendicular to the…

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Q: Find the volumes of the solids The base of the solid is the region in the first quadrant between the…

A: The base of the solid is the region in the first quadrant between the line y = x and the parabola y…

Q: Having been asked to design a brass plumb bob that will weigh in the neighborhood of 180 g, you…

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Q: e volume of the solid generated by revolving the shaded region about the x-axis. 3x + 4y = 24 10 The…

A: Topic:- application of integration

Q: The region bounded by the graph of y = 2x-x and the x-axis is the base of a solid. For this solid,…

A: Given the curve, y=2x-x2. The base of the solid is bounded by the graph of the given curve and…

Q: A solid formed when the area between y=2x2 and the x_axis over the interval 0≤x≤2 is rotated about…

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Q: urrent Attempt in Progress Use cylindrical shells to find the volume of the solid generated when the…

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Q: We model pumping from spherical containers the way we do from other containers, with the axis of…

A: To find the amount of the work.

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: The base of a solid is the region in the first quadrant bounded by the curves below. 16x 16 – y? %3D…

A: We need to find the volume of the solid.Below find the solution in the image.

Q: Locate the centroid of the shape shown. Use r= 15cm. X a. What is the y-coordinate of the centroid…

A: Given- Locate the centroid of the shape below. Use r = 15 cm To find-  What is the y-coordinate of…

Q: A hemispherical tank of diameter 8 ft. is full of liquid. Find the work done in pumping the liquid…

A: Given:- diameter 8 ft. radius r=d2=82=4 ft Volume of hemisphere=23πr3   Volume of hemisphere=23π43…

Q: A company has been asked to design a storage tank for LPG. The tank the customer wants, the middle…

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Q: An engineer is designing a part for a prototype. A 3D printer is able to take the engineer's…

A: The height of triangle is 5mm so cone of height 5mm can be created.