8.2 Area of a Surface of Revolution Review

dS =

2 πr dℓ

Let C be a finite curve lying above the x-axis. If C is revolved about the x-axis, the surface of an infinitesimal truncated cone at would be

dS = 2 π y dℓ

If the curve C is revolved around x-axis and defined by y = f(x), a<= x <=b, then dℓ = sqrt(1 + (f’(x))²) then S =

S = int (bounds a, b)(2 π f(x) sqrt(1 + (f’(x))²)

If the curve C is revolved around x-axis and defined by x = g(y), c<= y <=d, then dℓ = sqrt(1 + (g’(y))²) then S =

S = int (bounds c, d)(2 π y sqrt(1 + (g’(y))²)

Let C be a finite curve lying to the right of the y-axis. If C is revolved about the y-axis, the surface of an infinitesimal truncated cone at would be

dS = 2 π x dℓ

If the curve C is revolved around y-axis and defined by y = f(x), a<= x <=b, then dℓ = sqrt(1 + (f’(x))²) then S =

S = int (bounds a, b)(2 π x sqrt(1 + (f’(x))²)

If the curve C is revolved around y-axis and defined by x = g(y), c<= y <=d, then dℓ = sqrt(1 + (g’(y))²) then S =

S = int (bounds c, d)(2 π g(y) sqrt(1 + (g’(y))²)