The surfaces ρ1 = 2, ρ2 = 5, φ1 = 100◦, φ2 = 130◦, z1 = 3, and z2 = 6 define a closed surface. Find (d) the length of the longest straight line that lies entirely within the volume. Draw the diagram.

Q: Find the area of the portion, for which z > T9, of the sphere in R° with radius /3 centered 2 at the…

A: Here we find the area.

Q: Let B be the solid whose base is the circle x^2+y^2=49 and whose vertical cross sections…

A: Given, Circle- x²+y²=49=7² --------equation 1 The equation is of the form x²+y²=r². Therefore, the…

Q: What is the volume of the solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y…

A: Given,  The solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y = x2 and x = y2

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

A:

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: What is the equation of the surface revolved about the x-axis for z? – xz = In x + 3x? A. y? + z? =…

A: Given that z2-xz=lnx+3x The objective is to write the equation of the surface revolved about x axis.…

Q: Find the area of the surface generated by revolving x = t+2/3, y = +2/3t+3, -2/3 sts2/3 about the…

A: The surface area of disk is s=πr2 h  where r is radius and h is width

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

A:

Q: Use the disk method to verify that the volume of a sphere is 4/3 πr3 , where r is the radius ?

A: So sphere is basically a circle that is rotated through the x-axis. We will suppose to cut a disk…

Q: Find the volume of the tetrahedron bounded by the plane z=4-4x-2y and the coordinate planes. I

A:

Q: Find the area of the surface generated by revolving x =t+ 2/5, y= +2/5t, -2/5 sts2/5 about the…

A: Here we will find out area of surface of revolution.

Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

A:

Q: Consider the surface shown in the following figure: If h, k, r, m, teR. A general equation that…

A: Solution is below

Q: Use the Theorem of Pappus and the fact that the volume ofa sphere of radius r  is 4/3πr3  to find…

A: We have, The volume of a sphere is V=43πr3                               ⋯⋯1. The semi-circular…

Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 9x +y +Z = 18 is ?

A: We want to find the volume of the tetrahedron enclosed by the co-ordinate planes, i.e. x=0, y=0, z=0…

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

Q: Find the area of the surface obtained by rotating the parabola 1 y = 0 <x < 2, about the y-axis.

A:

Q: If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = c, where f(x) ≤ c, find a…

A: Given, Curve y= f(x) , a≤x≤b Rotated about a horizontal line y=cwheref(x)≤c

Q: The volume of the solid given by the two surfaces is z = 8 - 3(x? + y*), z = (x? + y")2 - 2

A:

Q: Show that the volume common to the surfaces 2 p2+z=4ax and x+y?=2ax is (3r+8)*. 3

A:

Q: Consider the paraboloid z = 1- ² – y?. Find the volume of the region between this surface and the ry…

A: According to the problem,. we have

Q: Find the volume of the region enclosed by the paraboloid (x-1)²+y? =z and the plane 2x+z=2.

A:

Q: Find the surface area if C = {(x, y): 1 ≤ x ≤ 2,y = about the x-axis.

A:

Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

A:

Q: f (x, уy) %3D — 3х — 2у + 6 | R = {(x,y) : 0 <x< 2,0< y< 2 – x )}

A: Given query is to find the area bounded by the region.

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: Find the area of the surface generated by revolving x = t+2/3, y =+2/3t+1, -2/3 sts2/3 about the…

A: Find the area of the surface generated by revolving the graph of the following parametric equation…

Q: Find the surface area for the portion of the hemisphere z =sqrt(4 − x^2 − y^2) that sits above the…

A:

Q: Use the polar coordinates to find the volume of a sphere of radius 3.

A:

Q: Determine the volume of the region that lies under the sphere x² + y² + z² = 4, above the plane z…

A: Given: Now,

Q: Evaluate the exact area of the surface obtained by rotating the circle x2 + y² = r² about the line y…

A:

Q: Find the approximate area of the surface obtained by rotating x = - (y° + 2)/², 1 sys2 about the…

A:

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

A:

Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

A:

Q: Use the change of variables formula to prove that the volume of the ellipsoid given by ()* + (#)* +…

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

Q: If the infinite curve y = eSX, x > 0, is rotated about the x-axis, find the area of the resulting…

A:

Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: y e 3x, x 2 0, is rotated about the x-axis, find the area of the resulting surface. If the infinite…

A: Find the area of the curve when rotated about x-axis

Q: Show that the volume of the segment cut from the paraboloid x2 /a2 + y2/ b2 = z/ c by the plane z =…

A: Show that the volume of the segment cut from the paraboloidX^2 /a^2 + y^2/ b^2 = z/ cby the plane z…

Q: Find the surface area of a sphere of radius r

A:

Q: Find the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

A: To the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

Q: find the surface area obtained by rotating the circle (x – 4)2 + y? =1 about the y-axis. %3D

A:

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is 32 3 9. 2 O…

A:

Q: For the conical surface 0 = 30°,0 <0< 21,0 <r< 2, the lateral surface area is what?

A: Sol

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

A:

Q: Find the area of the surface obtained by rotating thecircle x2 + y2 = r about the line y =r.

A: We have to find the area of the surface obtained by rotating the circle x2 + y2 = r about the line y…

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

A:

Q: By rotating the line y = r about the x-axis, for x in the interval [0, h], and applying the surface…

A:

Q: The exact area of the surface obtained by rotating the following curve 6x = y + 12, 2 < x < 3 about…

A:

Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: We know by the theorem of Pappu that the volume of a solid is obtained by area times the distance…

Q: Use the disk method to verify that the volume of a sphere is (4/3)π r3 , where r is the radius.

A: Volume of sphere of radius r is (4/3) πr3

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…