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SOLVED:Use a surface integral to show that the surface area of a sphere of radius r is 4 πr^2, Hint: Use spherical coordinates to parametrize the sphere.)

SOLVED:Use a surface integral to show that the surface area of a sp…

How to Find the Surface Area and Volume of a Sphere

How to Find the Surface Area and Volume of a Sphere

WonderHowToDonna Blankenbecler

SOLVED: Evaluate the surface integralâˆ«SFâ‹… dSwhere F=âŒ©âˆ’5x,4z,âˆ’4yâŒªand S is the part of the spherex^2 y^2 z^2=16in the first octant, with orientation toward the origin.âˆ«âˆ«SFâ‹… dS=

SOLVED: Evaluate the surface integralâˆ«SFâ‹… dSwhere F=âŒ…

SOLVED:Evaluate the surface integral ∬s 𝐅 ·d 𝐒 for the given vector field 𝐅 and the oriented surface S . In other words, find the flux of 𝐅 across S . For closed surfaces, use the positive (outward) orientation. 𝐅(x, y, z)=x 𝐢 y 𝐣 z^2 𝐤, S is the sphere with radius 1 and center the origin

SOLVED:Evaluate the surface integral ∬s 𝐅 ·d 𝐒 for the given vecto…

21-32 Evaluate the surface integral. 𝐅(x, y, z)=x 𝐢-z 𝐣 y 𝐤, S is the part of the sphere x^2 y^2 z^2=4 in the first octant, with orientation toward the origin | Numerade

21-32 Evaluate the surface integral. 𝐅(x, y, z)=x 𝐢-z 𝐣 y 𝐤, S is the part of t…

Surface Area of a Sphere | Formula, Calculation & Examples

Surface Area of a Sphere | Formula, Calculation & Examples

46K viewsMay 30, 2019

A sphere of radius R has total charge Q. The volume charge CALC density (C / m^3) within the sphere is ρ(r)=C / r^2, where C is a constant to be determined. a. The charge within a small volume d V is d q-ρd V. The integral of ρd V over the entire volume of the sphere is the total charge Q. Use this fact to determine the constant C in terms of Q and R. Hint: Let d V be a spherical shell of radius r and thickness d r. What is the volume of such a shell? b. Use Gauss's law to find an expression for

A sphere of radius R has total charge Q. The volume charge CAL…

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