The region bounded by the curve y= x² and the line y=3x is revolved about a) x-axis b) y-axis c) the line x=-3 d) the line y=-1 Find its volume generated in each case by two methods.

Q: 2. Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y…

A: The bounded region: Green colored    To find: The volume of revolution around y-axis of the bounded…

Q: If the volume of the solid obtain by rotating the region enclosed by the curves y = 2 x2 and y = 0…

A: Integration of curves help us to find volume of curves or area under the curve. It becomes quite…

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: Find the volume of a solid where the base of the solid is  a circle with radius 2, and the cross…

A: Let the circle be centered at origin and the radius is 2.

Q: 4. Use cylindrical shells to find the volume of the solid that is generated when the region that is…

A:

Q: 8. Find the volume of the solid whose base is the semicircle y = V9 – x², where -3 sIS 3, and whose…

A: This question is based on application of integration.

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x? = 8y,…

A:

Q: A metal plug has been designed using the intersection of the two cones z = √√x² + y² and √x² + y² +…

A:

Q: Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 5), and (5, 0).…

A: Sketch the base of the solid as follows.

Q: Find the volume generated by the revolving the region bounded by y = x, and the lines y = 3, and x =…

A:

Q: 2. bounded by the axis of the region Volume of the body of rotation created by rotating it Oround ?

A: Given that  y = 1 -x2, x =0 , y = 0   x2 = 1- y The limits of y :-  from y = 0 to y = 1

Q: Find the volume generated by revolving the area 1 bounded by y -, x = 2, x = 4, and y = 0 about the…

A:

Q: The cube is 3cm on one edge. Each of these joints A and B is 1cm from the vertex nearest it. If two…

A: This question is based on 3-D volume calculation in whivh two plane cut a wedge from a cube. We got…

Q: 2. Find the volume of he solied nohose base is Ine region bounded by y-x And y=1-x2, and whose are…

A: The points common to y=x2 and y=1-x2 can be calculated as: x2=1-x22x2=1x2=12x=±12 So the integral is…

Q: Use the Theorem of Pappus to find the exact volume of a general cone created vertices (0, 0), (1,0),…

A:

Q: Find the volume produced by rotating the region bounded by the circle x ^ 2 + y ^ 2 = 9 from the…

A: Solve :

Q: If the path defined by z(x) from points C to W were rotated about the x-axis, what would be the…

A: Given zx=-0.00001x6+0.00026x-0.00313x4+0.01704x3-0.01298x2-0.30265x+3.56157 To find the volume of…

Q: Consider a right-circular cylinder of diameter 1. Form a wedge by making one slice parallel to the…

A: The diameter of the right circular cylinder is d=1. The angle which is made by other slide to the…

Q: What is the volume (in πcu. units) of the region bounded by the curve y=x^3, and the lines x=1, x=2…

A:

Q: Determine the surface area formed by revolving the shaded area 360∘ about the z axis.

A:

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

A:

Q: 4- Find the volume of the solid generated by revolving the region about y-axis,the region in the…

A: Draw the graphs of y=x2, x=2 and identify the region bounded by the curves. The required region is…

Q: Find the volumes of the solids whose bases are bounded by the circle x^2+y^2=4, with the indicated…

A: Given, x2+y2=4 Part a: We have, x2+y2=4⇒y2=-x2+4⇒y=±4-x2 Now we find the area to use in finding the…

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

A:

Q: (c) Semicircles (d) Isosceles right triangles y 2)

A: Part C) To find the volume of the solid whose bases are bounded by the circle x2+y2=4,  And the…

Q: The region bounded by y = 2x – x2, and y = 1 is revolved about: 1- The line x = 1 2- The y-axis Find…

A:

Q: Find the volumes of the solids generated by revolving the region about the given line (a) y = x¹, y…

A: We will identify the region bounded  and then generate solid by revolving it about line x=-2 . To…

Q: By using shell method, find the following volume a. y = (x-3)2 and line y = -2x + 6 about x axis

A: Two functions are given by y=x-32 and y=-2x+6. The objective is to find the volume bounded by the…

Q: Find the volume of the region E 3 = {(x, y, z) : æ² + y? – 3 < z < v 9 – x² – y² } - - -

A:

Q: Find the volume generated by the revolving the region bounded by y = x, and the lines y= 3, and x =…

A:

Q: By using shell method, find the following volume a. y = x2 - 4x - 4 and line through point A(1,3)…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the volume of region revolving about y axis, and bounded by x-axis and 4 Vx 8 y = ,0 < y < 3 1…

A: I use shell method to find volume about y axis

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: 1. Use cylindrical shells to find the volume of the solid generated when the shaded region is…

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

Q: Determine the volume generated about y = 4, the area bounded by x + y = x? %3D and x? + y = 3.

A: To find the find the volume about y =4 Given x + y = x^2 , x^2 +y = 3

Q: 2 Eualuate the inteyral 22 -- taken. throughout the volume • f sphere

A:

Q: Determine the volume generated by revolving the region bounded by the lines y = 4 - x, x = 0, and y…

A:

Q: (4) Find the volume of the solid obtained by rotating the region bounded by y = r, y = 0, x = about…

A: Given:- y=x3,  y =0 and x=1 To find:- Volume of solid about line x=2

Q: Find the volumes of the solids formed when the region bounded by y = 0 and y = 1/x, between x = 1…

A:

Q: Find the volume generated by revolving the area 1 bounded by y -, x = 3, x = 9, and y O about the…

A:

Q: 9. Find the demensions of the right circular cylinder of largest volume that can be inscribed in a…

A:

Q: The area bounded by the curve y = e−x, the axes, and the line x = 2 is revolved around ox. Find the…

A:

Q: 2 Find the volume of the salid in the by the Coordinates planes, the plane x=3 , and the parabolic…

A:

Q: . Find the volume bounded by z = 9 –x² – y² and z = 0. Give a numerical %3D answer.

A: Given that the region is bounded by z=9-x2-y2 and z=0. We know that the volume bounded between…

Q: A hole is drilled through the center of a ball of radius r, leaving a solid with a hollow…

A: Given  that the center of a ball of radius r;  and  the  height of the cylinder be…

Q: 5. Use cylindrical shells to find the volume of the solid generated when the region enclos between x…

A: The formula for the volume of the solid generated by a curve using the shell method is given by…

Q: 5. Find the volume generated by the areas bounded by the straight line y = x, between y = 0 and x =…

A:

Q: Find the volume generated by revolving the area bounded by : 2, x = 5, and Ж — x3 + 9x² + 18x y = 0…

A:

Q: Right circular cones of height h and radius r are attached to each end of a right circular cylinder…

A: Let Vcr be the volume of the cone and Vc be the volume of the cylinder. So, Vcr=πr2h and Vc=13πr2h.