given a circle of radius a, find by integration using polar coordinates (a) its area (b) the centroid of one quadrant (c) the moment of inertia of a circular lamina aout a diameter (d) its circumference (e)the centroid of a quarter circle arc

Q: a] A right circular conical tank  of height 8 ft and radius 3 ft across the top, is filled with…

A:

Q: The limits of integration of p in spherical coordinates to find the volume of the

A: Given, Volume of the region bounded below by the cone z=4x2+4y2 and above the plane z=2. Volume of…

Q: The limits of integration of p in spherical coordinates to find the vohume of the region bounded…

A: cartesian to polar conversion x = ρ.cosθ.sinϕy = ρ.sinθ.sinϕz = ρ.sinϕ

Q: A ring is formed by rotating the shaded area 360° about y-y axes. Determine (1) its surface area and…

A: We find the surface area and volume

Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. y =…

A:

Q: In cartesian coordinate system, differential volume element is dxdydz. Infer the differential volume…

A: Concept:

Q: A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 6…

A: answer is in next step

Q: A 1.5-mm layer of paint is applied to one side of the following surfaces. Find the approximate…

A: The given equation of circle is x2 + y2 = 100. This can be written as Thus, the upper portion is

Q: 2. Find the volume of the solid formed by the region inside the sphere x2 + y² + z² = 16 and outside…

A: Here we have to find the solid volume formed by the region inside the sphere x2+y2+z2=16 and outside…

Q: Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the…

A:

Q: Calculate the volume of the region whose boundaries are indicated below. tip: use cylindrical…

A: Given Z=-y Z=0 to z = 3costheta

Q: over the region E inside x +y +z = 4 in the first octant. Convert the point (2, 2, -2v2) rectangular…

A: We have been given the cartesian coordinates (2, 2, ). We have to convert these cartesian…

Q: The limits of integration of p in spherical coordinates to find the vohume of the region bounded…

A: Consider the given region. z=3x2+3y2 and z=3 The spherical coordinates are defined as.…

Q: 10 y = 5x 5 0.5 1 1.5

A: Note:- As per your demand we solve question 9 fro you  Given:- y =5x ,y=5 ,y=10 To find:- Volume of…

Q: y = 3cos(x/2) the y axis and the x axis in the 1st quadrant revolved about the x-axis.

A:

Q: use a theorem of Pappus to find the centroid of the given triangle. Use the fact that the volume of…

A: By the theorem,

Q: The limits of integration of p in spherical coordinates to find the vohume of the region bounded…

A:

Q: Use cylindrical coordinates. Evaluate (Three integral signs with an E on the bottom of the last)…

A:

Q: Determine the location of the centroid,C of the beam's cross-sectional area.Neglect the size of the…

A: Consider the following: The sphere 1 with diameter 35mm. The rectangle with length 110m and breadth…

Q: Find the work required to pump the water out of a tank shaped like an upside down pyramid with…

A: We are asked to find the work done to pump the water out of a tank that is shaped like an…

Q: The volume of the rotating body formed by rotating the curve given by the x = 3cost y = 3sint, 0…

A:

Q: Find arc length and the surface area generated by rotating. x2 1 y +-;1< x < 2, around y – axis - 3…

A: Given that y=x23+1x, 1≤x≤2 around y axis. The formula for arc length is L=∫ab1+dydx2dx…

Q: Present a problem with solution solving the centroid of a solid of revolution using the circular…

A:

Q: Find the centroid of the area of a trapezoid that has two equal slanting sides, a 6 cm base and a 3…

A:

Q: 2. Use spherical coordinates to find the volume of the solid that lies above the 1 x² + y² and below…

A: 2) Soild is bounded above by 3x2+y2+z2=Zbounded below by ℤ =x2+y23sphere:…

Q: 1. Given a circle of radius a, find by integration using polar coordinates (a) its area; (b) the…

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

Q: use a parametrization to express the area of the surface as a double integral. Then evaluate the…

A:

Q: For the plane area shown, a) Locate the centroidal x- and y-axis b) Calculate the moment of inertia…

A:

Q: (a) find the spherical coordinate limits for theintegral that calculates the volume of the given…

A: To Determine: (a) find the spherical coordinate limits for theintegral that calculates the volume of…

Q: The given curve is rotated about the x-axis. Set up, but do not evaluate, an integral for the area…

A: When a curve y = f(x) is rotated about x axis on the interval a ≤ x ≤ b then area is given by- A =…

Q: Use a parametrization to express the area of the surface as a double integral. Then evaluate the…

A: The portion of the cone is given as z=3x2+y2 between the planes z=0 and z=12. Let us parametrize the…

Q: Use spherical coordinates to find the volume of a ball with radius R(in other words, use spherical…

A:

Q: A sphere of radius is drilled a cylindrical hole of radius b. Please find the remaining volume. Need…

A: In the question it is asked to calculate the remaining volume when a cylinder is cut out from a…

Q: Use polar coordinates to evaluate: a) SSRdA/(x²+y²+1) where R is the region in the upper second…

A: The value of the given region is (π/4)ln(2)

Q: The sphere of radius a centered at the origin is expressed in rectangular coordinates as x? + y? +…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: When we rotate a thin vertical strip as shown in figure, about the line y=-1. We get washer with…

Q: (a) Consider a solid under the plane z = 3 - x - y that lies above the circle r+y = 4 in the first…

A:

Q: Find the volume of rotated Gaussian about z-axis in cylindrical polar coordinates?

A:

Q: The area under the curve 4y2 = (x? + 1)3 was rotated about a line located to the left of y - axis by…

A: The area under the curve 4y2=169x2+13 is rotated about a line located to the left of y-axis by three…

Q: the volume of the Soli Find the volume. of the Solid of revolucton tor med by rolaing bout the…

A: The formula for calculating the volume of solid of revolution formed by rotating curve f(x) about…

Q: An ellipsoid is given by the equation 4x + 4y+z = 16; O Sketch the three-dimensional (3D) graph of…

A: Given,

Q: 1- In cartesian coordinate system, differential volume element is dxdydz. Infer the differential…

A: For this we will use the relationship of rectangular coordinate system with the spherical coordinate…

Q: 40. The y-axis x = tan y

A:

Q: Determine the x- and y-coordinates of the centroid of the shaded area. 55 130 Answers: -55 (X, Y) =…

A: Here we will use concept of  centroid of a combined shape, centroid of a combined shape= sum the…

Q: In cartesian coordinate system, differential volume element is dxdydz. Infer the differential volume…

A: The Spherical Coordinate system is: x=ρ sin(ϕ) cos(θ) y=ρ sin(ϕ) sin(θ)z=ρ cos(ϕ)

Q: Sketch and shade the region R. Hence, Calculate the area R. Then, Find the volume of the solid…

A:

Q: Find the volume and centroid generated by revolving the given plane area about y^2=4x, y=2x-4 ;…

A:

Q: Use spherical coordinates and integrate to find the area of the region 0≤φ≤βon the spherical shell…

A: the spherical shell of radius. to find the area when β= 2π e follow the procedure as

Q: A right circular cone is generated by revolving the region bounded by            y = 3x/4, y = 3,…

A:

Q: on the same axes, the curves y = 6- e and y= 5e coordinates of the points of intersection. Calculate…

A: Consider the given given function. y=6-ex and y=5e-x Now, draw the both graphs.