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ΔA Δx |
= 2πy | Δs Δx |
dA dx |
= 2πy | ds dx |
ds dx |
= √(1 + (dy / dx)^{2}) |
dA dx |
= 2πy√(1 + (dy / dx)^{2}) |
Surface area = | ∫ | x2 | 2πy√(1 + (dy / dx)^{2}) dx |
x1 |
y = x | r h |
Surface area of the cone = | ∫ | h | 2πy√(1 + (dy / dx)^{2}) dx |
0 |
y = x | r h |
so we can see that | dy dx |
= | r h |
Surface area of the cone = 2πr / h | ∫ | h | (x√(1 + (r / h)^{2}) dx |
0 |
Surface area of the cone = 2πr / h((h^{2} + r^{2})/h^{2}) | ∫ | h | x dx |
0 |
Have you found an error or do you want to add more
information to these pages? You can contact me at the bottom of the home page. |