Find the following using curvilinear coordinates a surface...

Name: find the following using curvilinear coordinates a surface area of a sphere of radius r b volume of a sphere of radius r c volume and surface area of the curved surface of a cylinder of leng 08724
Uploaded: 2022-05-06T16:47:06-08:00
Duration: 3 min 42 s
Channel: Frank Deng
Description: find the following using curvilinear coordinates a surface area of a sphere of radius r b volume of a sphere of radius r c volume and surface area of the curved surface of a cylinder of leng 08724

Find the following using curvilinear coordinates (a) Surface area of a sphere of radius R (b) Volume of a sphere of radius R (c) Volume and surface area of the curved surface of a cylinder of length L and radius r.

Transcript

00:01 Now in this question, you are giving a vector, right? let me write down the vector.

00:10 This vector is called a is given by, it's in the x direction, and it has a magnitude which is y plus x, right? and then you ask you to transfer this vector to synodicular coordinates, and then you evaluate it at a point, right? so synitry coordinates, that means basically you write, basically you just write x equals r cosine theta and y equals r celsius, right? that's what you do.

00:48 So you just write it as x r cosine theta plus r cata, right? that's what you get.

00:56 Or you can rewrite it as x, r, sancid, plus, cosine, theta, that is sans ceta plus consensata, right? so that would be the expression for this factor in cylindrical, in cylindrical coordinates.

01:12 And you value it at a point p equals, at a point p equals 1, 2, 3, right? that is why you just, that means, it does not really depend on the x, right? so sorry, it does not really depend on the z convert.

01:37 So you only look at the x and y, right? so if you read it at this point, you just plus x plus x here and plus y here.

01:44 So you'll find a at that point is given by x.

01:48 And 1 plus 3, that's 3, right? so 3 times x.

01:52 So that's a legged at that point.

01:54 Then next to you ask to convert the coordinates and the foreign point from a catents into 3 coordinates.

01:59 So the coordinate you are giving in the second part of the question is minus 2 to 2, right? and you ask you to transform into three coordinates...

Question

Find the following using curvilinear coordinates (a) Surface area of a sphere of radius R (b) Volume of a sphere of radius R (c) Volume and surface area of the curved surface of a cylinder of length L and radius r.

Please give Ace some feedback