Describe the Solid Using Spherical Coordinates

X ρ sin φ cos θ 8 sin π 6 cos π 3 8 1 2 1 2. C Consider figure a shown below.

Solved Example 4 Use Spherical Coordinates To Find The Chegg Com

The cone is z 3 x 2 y 2.

. A sphere that has Cartesian equation has the simple equation in spherical coordinates. Your final answer must be written in set-builder notation. This means that the iterated integral is Z 2ˇ 0 Z ˇ4 0 Z 1 0 ˆcosˆ2 sindˆdd.

Position the solid on the coordinate system such. X ρ sin φ cos θ 8 sin π 6 cos π 3 8 1 2 1 2 2 y ρ sin φ sin θ 8 sin π 6 sin π 3 8 1 2 3 2 2 3 z ρ cos φ 8 cos π 6 8 3 2 4 3. 0 φ π 4 0 φ π 4.

A portion of the sphere of radius 3. θ is the same angle used to describe the location in cylindrical coordinates. Describe using spherical coordinates the solid E in the first octant that lies above the half-cone zx 2 y 2 but inside x 2 y 2 z 2 1.

A portion of the z sphere of radius 3. Also for each θ ϕ the value of ρ ranges from 0 until the surface of the cone. ρ x 2.

B Describe the solid using cylindrical coordinates. B Convert the point 112 1 1 2 from Cartesian to spherical coordinates. Cartesian Cylindrical Spherical Cylindrical Coordinates x r cosθ r x2 y2 y r sinθ tan θ yx z z z z Spherical Coordinates x ρsinφcosθ ρ x2 y2 z2 y ρsinφsinθ tan θ yx z ρcosφ cosφ x2 y2 z2 z.

So were talking about a cube um that immediately should ring a bell. Spherical coordinates are a set of three numbers that form an ordered triplet and are used to describe a point in the spherical coordinate system. Homework Equations ρ x 2 y 2 z 2 x ρsinφcosθ y ρsinφsinθ z ρcosφ The Attempt at a Solution.

If frhotheta varphi is continuous on a spherical solid box B ab times alphabeta times gamma psi then. Consider the solid in R3 shown in Figure 1110. Use the formulas in 8 to express i j k in terms of er ee and ez.

Use the formulas in 9 to express i j k in terms of ep eq and ee. X ρ sinφcosθ y ρ sinφsinθ z ρ cosφ 2 y 1 2 x x y 122 2 z z 1- x - y2 2 z x y2 The top surface is the sphere ρ 1. So clearly 0 θ π and 0 ϕ π 2.

Describe the solid using spherical coordinates. X ρ cos. By first converting the equation into cylindrical coordinates and then into spherical coordinates we get the following z r ρ cos φ ρ sin φ 1 tan φ φ π 4 z r ρ cos φ ρ sin φ 1 tan.

So we know that this would be in the rectangular coordinate system. So the spherical coordinates of this point will are 2 2 π 4 π 3 2 2 π 4 π 3. Describe the solid using cylindrical coordinates.

That a cube is a form of a rectangle rectangular prison where the sides are equal. The other way to get this range is from the cone by itself. Spherical coordinates in R3 Example Use spherical coordinates to express region between the sphere x2 y2 z2 1 and the cone z p x2 y2.

The first thing that well do here is find ρ ρ. A Describe the solid using spherical coordinates. Spherical coordinates use the radial distance the polar angle and the azimuthal angle of the orthogonal projection to locate a point in three-dimensional space.

Fubinis Theorem for Spherical Coordinates. Use the equations in Converting among Spherical Cylindrical and Rectangular Coordinates to translate between spherical and cylindrical coordinates Figure 2100. Often important for us to be able to understand how we can use coordinates to describe a solid.

For the remaining problems use the coordinate system Cartesian. Describe the solid in spherical coordinates. In geography latitude and longitude are used to describe locations on Earths surface as shown in.

ρ cosφ q. Although the shape of Earth is not a perfect sphere we use spherical coordinates to communicate the locations of points on Earth. ρ the Greek letter rho is the distance between P and the origin ρ 0.

The bottom surface is the cone. So the solid can be described in spherical coordinates as 0 ˆ 1 0 ˇ 4 0 2ˇ. Problem 102 Easy Difficulty.

We can describe a point P in three different ways. I graphed the solid and it looks like this. Find inequalities that describe the solid and state the coordinate system used.

ˆ 1 in spherical coordinates. In the spherical coordinate system a point P in space Figure 1279 is represented by the ordered triple ρ θ φ where.

Solved Use Spherical Coordinates To Find The Volume Of The Chegg Com

Solved Example 4 Use Spherical Coordinates To Find The Chegg Com

Solved Example 4 Use Spherical Coordinates To Find The Chegg Com