MathGeek99
contestada

(30 pts.) I have the answer I just need someone to show me the steps, please!

Which bowl holds more water if it is filled to a depth of four​ units?
The hyperboloid z= √(1+x^2+y^2) for 1≤ z ≤ 5
The answer is: The hyperboloid holds more water with a volume of [112π/3]

I just need an explanation!!
5 stars and marked the brainiest if the explanation is done well!!

Respuesta :

zhiyanawilliams02

paraboloid: v = ∫[0,4]πz dz = 8π cone:

v = ∫[0,4]πz^2 dz = 64/3 π

hyperboloid: v = ∫[1,5]π(z^2-1) dz = 112/3 π


 when you see that the cone's radius at the top of the water is √8, while the paraboloid's is only 2.


hope it helps.

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