h R1 Area of R1 = area of R2

Q: 3. Find the exact value of surface area of the solid that is described by the intersection of the…

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Q: 1) Find the volume of the solid bounded by the poraboloid ze40-x-y, the cylinder xry2-20 and E) too…

A: Given that, Paraboloid is, z = 40 - x2 - y2 and cylinder is, x2 + y2 = 40 We have to find volume…

Q: The volume V of the parallelopiped that has u, v, w as adjacent edges is given by: V = |u. (v × w)|.…

A: We have to find

Q: Find the volume of the solid that is bounded on the front and back by the planes x = 1 and x = 4, on…

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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: 2) Find the volume of the solid bounded by the cylinder x2 + y = 16 and from z = 1 to z + x %3D 2…

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Q: The volume of the solid under the plane 4 x+ 5 y - z=0 and above the region enclosed 27 by y= 3 x…

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Q: 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y –…

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Q: A cylindrical container with both ends closed has a radius r cm and a volume 100 cm³. Determine the…

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Q: A volume is described as follows: 1. the base is the region bounded by æ = – y² + 2y + 98 and æ 2.…

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Q: Which of the following conditions do not have to be met to prove two solids have equal volumes using…

A: Given query is to find the condition which is not required to prove volume of solid are equal.

Q: Prove that if a sphere is inscribed in a right circular cylinder whose height is equal to the…

A: Since the height of the cylinder is same as the diameter of the cylinder or hat of the sphere so…

Q: 1 and the sphere Find the volume of the solid that lies inside both the cylinder x + y : x2 + y? +…

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Q: By integrating all three surface elements of a cylinder, find the surface area of a cylindrical pie:…

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Q: A box with square base and no top has volume 10 cubic units. If æ is the width of each side of the…

A: The given data is: Volume of box= 10 cubic units Width of the square base = x units The value of x…

Q: The base of a three-dimensional figure is bound by the line y = -2x + 5 on the interval [-1, 2].…

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Q: If the volume of the region bounded above by z = a2 − x2 − y2, below by the xy−plane, and lying…

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Q: 3. Find the volume of the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + %3D y + 2z =…

A: Will use the triple integration to find the volume of the tetrahedron which is bounded by the given…

Q: The base of a solid is the triangular region bounded by the y-axis and the lines 2x + 3y = 6 and 2x…

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Q: Each of the twelve edges of a cube of edge 2 cm is tangent to a sphere. Find the volume of that…

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Q: 10. Find the volume of the solid whose base is bounded by the graphs of the equations given below…

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Q: The base of the solid S is the region enclosed by the graph of y=sqrtln(x), the line x=e and the…

A: Given The base of the solid S is the region enclosed by the graph of y=sqrtln(x), the line x=e and…

Q: The volume of the body is given by the two surfaces sA z = 8 – 3(x² + y²), z = (x² + y²)² – 2 |

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Q: b) Find the volume of the solid which is in the first octant and bounded between the spheres p = 1…

A: To find- Find the volume of the solid which is in the first octant and bounded between the spheres ρ…

Q: If the region R = {(x, y) | x > 1, 0 < y < 1/x} is rotated about the x-axis, the volume of the…

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Q: The volume of the solid bound by the two surfaces is z = 8- 3(x² +y?), z= (x² + y?)² - 2.

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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: Construct a cylindrical container without the top to hold a volume 1m3.  What is the smallest…

A: Volume of cylinder = πr2h = 1 m3 Here, the cylinder is without top.

Q: Suppose that a region R has area A and lies above the x-axis. When R is rotated about the x-axis, it…

A: Use the disc method to find the W in terms of V, k and A.

Q: (d) Consider the parallelepiped P in R³ whose adjacent sides are (0, 4, 0), (3, 0, 0) and (-1, 1,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

A: Sphere was cut at height h, radius of the circle at intersection of 2 cuts is r2-h2. Similarly…

Q: Determine the volume of a four dimensional unit sphere: x, =r sin 8, sin 8, cos p, x, =r sin 0, sin…

A: The given problem is to find the volume of four dimensional unit sphere, we have to set up an…

Q: 5. Find the volume under the paraboloid z = -x² – y², and above the cone z = -. -V#²+ y².

A: Given

Q: - Find the volume of the solid that is bounded above by the cylinder z = 4-x2, on the sides by the…

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Q: Suppose a solid has a square based centered on the x-axis, and one of the base's edges follows the…

A: given function is fx=x5 , 0,6find the volume of the solid

Q: 5. Compute the volume of the region outside of the cylinder r² +y² = 16 and inside the sphere x2 +…

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Q: (a) COMPUTE the dimensions of the rectangular box of maximum volume that can be x² + y? + z? = 4.…

A: Since you have posted multiple questions, we will solve only first question for you. To get…

Q: A solid is constructed so that one side is the region between the lines z = a, x = b, the graph of y…

A: The volume of solid can be given by the formula V=∫Adx, here A  is the area of the region. The value…

Q: The base of a three-dimensional figure is bound by the line y = -2x + 5 on the interval [-1, 2].…

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Q: Compute the volume of an object covered within a region R=[-1,4] × [2,3] %3D and z = 9y – 4x using…

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Q: The base of a solid is the triangular region bounded by the y-axis and the lines 3x + 2y = 6 and 3x…

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Q: Find the constant k > 0 such that the volume of the region lying inside the sphere x2 + y2 + z2 = a2…

A: Given that,k&gt;0 is a constant such that the volume of the region lying inside thesphere…

Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ =…

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Q: 4. Find the exact value of surface area of the solid that is described by the intersection of the…

A: For a function, z=f(x,y) the surface area is calculated using the formula below. S=∬D[fx]2+[fy]2+1dA

Q: The surface area of a right-circular cone of radius e and height h is S – aryr² + h², and its volume…

A: Let r be the radius and h be the height of a right-circular cone then its surface area and volume is…

Q: If the volume of the region bounded above by z = a²-x² - y2, below by the xy-plane, and lying…

A: Please see the attachment

Q: Determine the volume of the largest rect an gu lar box in the first oct ant with three faces in the…

A: Given: The volume of the largest rectangular box is to be determined based on the first octant with…

Q: The volume of the tetrahedron bounded by the plane * ++ = :1, {a, b, c > 0} and the coordinate a…

A: Volume of the figure will be given by integral - V = ∫∫∫dzdydxLet's find limits of z,y and x - Given…