Show that the volume of a spherical block can be approximated by ∆V ≈ ρ2 sin ϕ ∆ρ ∆ϕ ∆θ.

Q: Use spherical coordinates to evaluate the mass of a solid given by the integral below: 2 To LT SVET…

A:

Q: (a) the volume of R using cylindrical coordinates with dV = r dz dr de w

A: NOTE:- According to the guidelines we cane solve only first question in case of multiple questions.…

Q: Find the mass of a wire of density δ(x,y,z) = kz if it has the shape of the helix C parameterized by…

A:

Q: The region under the curve y = x2 – x between a = 1 and æ = 3 is revolved about the line a = 3.…

A: SHELL METHOD TO FINDING THE RADIUS OF REVOLUTION ABOUT THE AXIS  x=3.

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

A:

Q: Suppose that a curved lamina o with constant density 8(x, y, z) = 8o is the portion of the…

A: mass=∫∫∫δx,y,z dv

Q: Q:4) Find the volume bounded below Zj= x²+y² and above by_Paraboloid Z; = 2-x²-y² by using…

A: We need to find the volume below Z1=x2+y2 and above by the paraboloid Z2=2-x2+y2 by using…

Q: The volume of the solid bounded by z = 0, x+y+z= 4 and x² + y² = 4 in cylindrical coordinates is 16.…

A: Solution:  True

Q: Verify the given moment(s) of inertia and find x and y. Assume that each lamina has a density of   =…

A:

Q: 1. What is the differential for the total surface area of a frustum of a cone with l as the slant…

A: Given slant height l. Let r and R be the radii of the frustum. Let h be the height of the frustum.…

Q: 2. Use spherical coordinates to evaluate the triple integral ||| æe xe²²+v²+z dV , where E is the…

A: Given:

Q: Compute the volume of the solid bounded by the hemisphere z = the horizontal plane z = c by using…

A: To compute the volume of the spherical cap, use the following formulae and convert the Cartesian…

Q: Sketch the region defined by the following two conditions (in spherical coordinates): 0<p<2, 0<¢s…

A: The region is: Given that 0≤ρ≤2, 0≤φ≤π4 The given region is a part of a sphere of radius 2.

Q: =) Given a lamina that occupies the region outside the circle r = 2 and inside the %3D cardioid r =…

A:

Q: Set up an integral in Cylindrical coordinates that represents the volume of the solid above the cone…

A: Converting rectangular coordinate into cylinderical coordinate.

Q: V=$t re h for r (geometry, volume of a spherical tuumor).

A:

Q: Given that D = zp coso a̟ C/m², calculate the charge density at (1, /4, 3) and the total charge…

A: Given that D=zρcos2ϕaz Charge density = ρv=∇.D where ∇=aρ∂∂ρ+aϕ1ρ∂∂ϕ+az∂∂z Now,…

Q: Set up an integral in Cylindrical coordinates that represents the volume of the solid above the cone…

A: A polar coordinate system contains a reference point (pole) and a reference direction (polar axis).…

Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A: The region is bounded by the graphs of the equation y=cosπx4, y=0, x=0 and x=2. The density is given…

Q: Evaluate the cylindrical coordinate integral: L L dzr dr de O 647 O 87 O 167 O 1287

A: To solve the integral

Q: Use cylindrical coordinates to evaluate SI vz dv where E is the solid E bounded by the cylinder,…

A:

Q: Let S be the boundary of a cube with side length 1 in octant 1. Use Stokes Theorem to evaluate Se…

A:

Q: Find the mass and center of mass of a wire in the shape of the helix x = t, y = 2 cos(t), z = 2…

A: Given :-  The mass and center of mass of a wire in the shape of helix x = t , y = 2 cos  t   ,  z =…

Q: In cylindrical coordinates, the integral r dz dr do represents the volume of a solid... in between…

A: Given ∫02π∫12∫01rdzdrdθ

Q: A large metal disk with radius of 2 m has been made. The density of the metal disk is given by p(r,…

A:

Q: Find the exact mass of a thin wire in the shape of the helix x = 2 sin(t), y = 2cos(t), z = 3t, 0 <…

A:

Q: ' ., Let G be the solid which lies above the plane z = V3 and within the sphere r + y + 2² = 4.…

A: We will use triple integral to find the volume then we will multiply it with the uniform density to…

Q: Compute the volume of the solid bounded by the hemisphere z = √4c²-r² - y² and the horizontal plane…

A: The given problem is to find the volume of the solid bounded by given hemisphere and plane by using…

Q: Consider the solid bounded by 4x² +y² +z? =9, and z> 4x? + y? with a Problem 8 constant density of…

A:

Q: Explain why dz r dr dθ is the volume of a small “box” in cylindrical coordinates.

A: (r,θ,z) are the cylindrical coordinates; here r, θ denotes the polar coordinates of the image of…

Q: Evaluate the cylindrical coordinate integral. бл 8 LL dzr dr de 4л 8

A: = ∫4π6π ∫48(9r-8r)rdrdz =∫4π6π(8-4)dz = 4(2π) = 8π

Q: What is the differential for the total surface area of a frustum of a cone with i as the slant…

A: The formula for total surface area of the frustum of the cone with the given slant height l is Total…

Q: Use a triple integral over spherical coordinates to evaluate (2² + y²) dV, where E is the sphere a²…

A: Volume of triple integral, using cylindrical coordinates

Q: luate the triple integral /// V² + y² + z² dV over the spherical shell E 9.

A: Integration using spherical coordinates

Q: Given a lamina that occupies the region outside the circle r = 2 and inside the 0, and has density p…

A:

Q: at Va:-x dz dy.dx

A: To convert the integral  ∫-aa∫-a2-x2a2-x2∫aa+a2-x2-y2zdzdydx to spherical and cylindrical…

Q: Given a lamina that occupies the region outside the circle r = 2 and inside the cardioid r = 2 +…

A: Given a lamina that occupies the region outside the circle r = 2 and inside the cardioid…

Q: Set up an integral in Cylindrical coordinates that represents the volume of the solid above the cone…

A:

Q: Let S be a square plate with boundary C, having each side of length 2 units, lying in the plane x =…

A:

Q: Find the volumes of the solids

A: We have,

Q: Find the Volume %3D ヒ= 2 cos 0,×2+yナz = 4.

A: The given problem is to find the volume of solid formed by given surfaces. Given surfaces…

Q: Find the exact mass of a thin wire in the shape of the helix x = 2 sin(t), y = 2 cos(t), z = 3t, 0 <…

A:

Q: Find the moment of mass from the x-axis for y = x In(x) – 3x and y density is equal to 0.37…

A:

Q: Consider where E is the region above the cone z = 2/+ y? and below the top of the sphere a+y 22 4.…

A:

Q: Set up an integral in Cylindrical coordinates that represents the volume of the solid above the cone…

A: Using spherical coordinates :

Q: Use spherical coordinates to calculate the volume of the region outside the sphere p = 2 cos Ø and…

A:

Q: Sketch the lamina S of constant density ρ = 3 g/cm2 occupying the region beneath the graph of y = x2…

A:

Q: 2r In cylindrical coordinates, the integral rdzdr d0 represents the volume of a solid... in between…

A: We will find out the required solution.