18. Find the surface area of the part of the sphere x² + y² + z² = 4 that lies inside the cylinder x? + y² = 2y. Sketch the given surface. 19. Find the surface area of the sphere x² +y² + z² = 9. Sketch the given surface.

Q: Find the surface area of the paraboloid z= 1 - (x2 + y?) that lies between the sphere x? + y? + z² =…

A: Given the region

Q: Calculate the surface area of the following: the cap cut from the sphere r² + y² + z² = 3 by the…

A:

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 exact area of the surface obtained by rotating the curve about the x-axis. 4x = y? + 20,…

A:

Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

A:

Q: Evaluate: I| (x2 + y?) ds over the surface S of the sphere x2 + y? + z? = 5. Use Formula (5.22a)…

A: The solution is given below:

Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

A:

Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: Ex.7 The area of the surface ∑ = {(x,y,z) €R® : (x² + ²) < 1, z = 9 + xy} is: (A) - 5 (B) 4개 2 (C)…

A: Using polar coordinates.

Q: 7. If the net was folded into a box, which sides represent the lateral surfaces? a f C e d

A:

Q: e surface generated by y=x^3 on [0,1], about the x-axis. Final Answer is A(s)=3.563 sq. units, Show…

A: Solution:- y=x3       0,1 y'=3x2 y'2=3x22y'2=9x4 Now find surface area S= ∫012πy1+y'2dx…

Q: Let S be the portion of the surface x -2x + y² + z² = 8 for 1<z<2. Find the area of the surface S.

A: x2-2x +y2+z2 =8 ⇒(x-1)2+(y)2+(z)2=(3)2 So the surface S is a circular patch of a circle canter at…

Q: 4 The area of the surface S = {(x, y, z) E R³ : z = 5 – z2 – y², z > 3} equals (A) 47 (B) 13 (C) (D)…

A:

Q: Compute 3xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

A:

Q: w.The given.surface.at. thespeeif 2.

A: Introduction:   We know that the equation of tangent plane to the surface z=f(x,y) at the point…

Q: Given the expression x* – 3x + 7 = y³. on the interval [3,5], determine the surface of revolution if…

A: Given; x4-3x+7=y3 on the interval [3,5]

Q: 4 The area of the surface S = {(x, Y, z) E R³ : z = 5 – x² – y², z > 3} equals (A) 4ñ 9. (B) 5* 13…

A: 4 Given S=x,y,z∈R3:z=5−x2−y2,z≥3.. We have to find the surface area of S At z=3 ⇒3=5−x2−y2⇒x2+y2=2…

Q: 18. Find the surface area of the sphere with radlus 5 by dou- bling the surface area of (x, y)…

A: Given: f(x,y)=25-x2-y2 is the surface bounded by the circle x2+y2=25 where radius, r=5

Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: Write down inequalities to represent (a) the region inside the sphere 2² + y² + 2² = 62 and outside…

A: The given problem is to find the inequalities that represent the given solids of region bounded by…

Q: Find the area of the surface for the portion of the sphere x+y +z = 225 inside the cylinder x-+y-=…

A: Given that  Sphere x^2+y^2+z^2=225  Cylinder x^2+y^2=144 To find the area of the surface

Q: Find the area of the part of the sphere x2+y2+z23D 9z that lies inside the paraboloid z =r+y?. a.…

A:

Q: Find the olume of the solid cut Prom the sphere 8=2C@SQ by the Cone Z= Jx+ ý Ans/ T

A: The given question is related with triple integral. We have to find the volume of the solid cut from…

Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

A:

Q: Find the surface area of the portion of the surface z = xy which is inside the cylinder p2 +3? = 9.

A: It is given that the portion of the surface is z=xy=fx,y. The surface area of the surface is…

Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

Q: ded above by surface z = 10 – x2, bou e planes y = 0 and y = 3.

A:

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

A:

Q: 7. Use a program to plot the surface generated by the following equation: 4x – 16y + z? = 16

A: we need to plot the following surface generated by, 4x2-16y2+z2=16

Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

A:

Q: 4 The area of the surface S = {(x, y, z) € R³ : z — 5 — z² - y², z ≥ 3} equals (A) 4T (B) (C) (D)…

A:

Q: Find the surface area of the part of the sphere x^2+y^2+z^2=49 that lies above the cone…

A: Given:

Q: Find the area of the cap of the sphere x2 + y² + z? = 2 cut by the cone z = Vx2 + y² |3D

A:

Q: 15r If F(r) = and o is the surface (r – 3)? + y +z? = 49 oriented outwards, what is the value of F n…

A:

Q: ind the area of the surface generated when the give curve is revolve about the x-axis    y=(x^3)…

A: Consider the given curve: Here the objective is to determine the area of the surface generated when…

Q: Find the surface area generated by rotating the semi-circle x = (49 – y² be- tween -7 < y < 7 about…

A: To Determine :-  The surface area generated by rotating the semi-circle x = 49 - y2 between -7 ≤y ≤7…

Q: 16. classify the surface: * 1- y? = 5x2 + 6z? Sphere Elliptic paraboloid Cone Plane Ellipsoid

A:

Q: S y = 3 – 2 4z – 4 = 3(x +1)?

A: Let us start solving the problem step by step

Q: 8. Draw the figure and Find the area of the part of the sphere x? + y? + z? = 3z that lies inside…

A:

Q: Given, w = f(x,y, 2) = y – Va² +2? Sketch the level surface for w = 0.

A:

Q: Find the area of the surface for the portion of the sphere x+y² +z* = 225 inside the cylinder x+y…

A:

Q: 15r = and o is the surface (x − 3)² + y² + z² = 49 oriented ||r||³ FndS? If F(r): outwards, what is…

A:

Q: Let be s a surface compaund by the union of s, qnd Sz An expression to get the Area of the Surface…

A:

Q: 11r If F(r) and o is the surface (x – 4)2 + y² + z² = 49 oriented 3 outwards, what is the value of…

A:

Q: Which surface has the following equation? x2 – 2y = 32 O Cylinder O Plane Paraboloid Hynerboloid

A: Please refer to the image below

Q: 15) Consider curve C which is the intersection of the surfaces shown in the attached figure. The…

A: The equation of the graphs given are as follows: x=-34y2+3y=yz=y22 We are asked to evaluate the…

Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

A:

Q: Find the surface area of a quarter of the sphere x? + y2 + z2 = 4.

A: The equation of a sphere centered at x0, y0, z0 is defined using the formula: x-x02+y-y02+z-z02=r2,…

Q: Find the area of the part of Sphere x? + y? + z? = 16 that is outside the paraboloid z=16 – x² – y?.…

A: The part of the object outside another object can be obtained by first calculating the intersection…