- #1
maupassant
- 10
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Homework Statement
Find the surface area of the cone with the following equations:
x= u sin(a)cos(v) , y= u sin(a)sin(v), z=u cos(a)
where 0<=u <=b , 0<=v<=2(pi), a is constant!
The Attempt at a Solution
Trying to solve this I first calculate the absolute value of the cross product of r'(u) and r'(v):
ABS(r'(u) x r'(v)) = SQRT(u^2 (sin(a) ^2)) = u sin(a)
Then I try to integrate this result by calculating
∫ ∫ (u sin(a)) du dv = ∫ (1/2)(b^2) (sin(a)) dv = (pi) (b^2) sin(a)
with 0<=u<=b and 0<=v<=2(pi) as limits of integration.
This result however does not correspond with the formula to find the surface area of a cone.
Could someone help out with this problem?
Thank you!
Homework Statement
Homework Equations
The Attempt at a Solution
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