Note: since surface area s= double integral |rt xrz|dA.
Using this formula we calculate the value of surface area.
Details explained in the image.
14. find surface area of S { (x,y,z) | x-3cost y-3sint z-z 14. find surface area of S { (x,y,z) | x-3cost y-3sint z-z
Let S be the ‘football’ surface formed by rotating the curve y =
0, x = cos z for z ∈ [−π/2, π/2], around the z-axis. Find a
parametrization for S, and compute its surface area. Please answer
in full With full instructions.
Let S be the 'football, surface formed by rotating the curve y = 0, x-cosz for-E-π/2, π/2], around the z-axis. Find a parametrization for S, and compute its surface area 3
Let S be the 'football, surface...
Find the area of the lateral surface over the curve C in 6. the xy-plane and under the surface z - f(x,y) f(x,y)-h, C:y-1 -x2 from (1,0) to (0,1) Surface: Lateral surface area - f(x, y) ds z =f(x, y) Lateral surface xy) As C: Curve in xy-plane
Find the area of the lateral surface over the curve C in 6. the xy-plane and under the surface z - f(x,y) f(x,y)-h, C:y-1 -x2 from (1,0) to (0,1) Surface: Lateral surface...
Find the length of the curve r(t) =< 3cost, 3sint, 4t > for 1 st 57.
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
#P2 The differential of surface area, ds, for a surface determined by the graph of z=f(x,y) is calculated by dS = #P3 The differential of surface area, dS, for a surface determined by the graph of x = f(y,z) is calculated by dS = #P4 True or false: If Fis a velocity vector field for some fluid and S is a semipermeable surface, then the flux integral JJs FindS computes how quickly volume is passing through the surface S.
Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = x2 + y2, R = {(x, y): 0 = f(x,y) 3}
find the surface area of that portion of the sphere x^2+y^2+z^2
= 25 that is below the xy-plane and within the cylinder
x^2+y^2=4
5. [10 Marks] Find the surface area of that portion of the sphere x2 + y2 2-25 that is below the ry-plane and within the cylinder 2 -4
Find the area of the portion of the plane 2x+3y+4z=28 lying
above the rectangle 1≤x≤3,2≤y≤5 in the xy -plane.
(1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22 < 36 Area(S)-
(1 poimi) Find the surface area of the portion S of the cone 22y, where z 20, contained within the cylinder y2 +22
(2) The area of the surface with equation z = f(x,y). (x,y) E D. where fra f, are continuous, is A(S) = SVGC3. y)]? + [f;(x, y)]? +T dA If you attempt to use Formula 2 to find the area of the top half of the sphere x + y2 + 2? = a, you have a slight problem because the double integral is improper. In fact, the integrand has an infinite discontinuity at every point of the boundary circle...
cc 5,16 55 55 f the surface generated by revolving x 44-y,0 s ysabout the y-axis. Find the area 16 . x=44-y The area is (Simplify your answer. Type an exact answer, using Tt as needed.)
cc 5,16 55 55 f the surface generated by revolving x 44-y,0 s ysabout the y-axis. Find the area 16 . x=44-y The area is (Simplify your answer. Type an exact answer, using Tt as needed.)