# Tagged Questions

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### Find depth of a half-filled parabolic cross-section

Given a cross-section of an object that is parabolic in shape, how do you find the depth of the object when it is "half full". A full example given in an exam: A long trough whose cross-section ...
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### How to determine the point at a set length along a given function (parabola)?

Given a specific function, a parabola in this instance, I can calculate the length of a segment using integrals to sum infinite right angled triangles hypotenuse lengths. My question is, can I reverse ...
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### Finding the volume of a cone by integration of parabolic conic sections

I am working on a purely academic way of finding the volume of a right circular cone of height $h$ and radius $r$, (assume $h > r$), using integration of parabolic conic sections (conic sections ...
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### Multivariable Calculus: Volume

Trying to figure out the following problem: Evaluate the integral $\int\int\int_EzdV$, where E lies above the paraboloid $z = x^2+y^2$ and below the plane $z=6y$. Round the result to the nearest ...
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### Finding a mass of elipse

I have a task, to find a part of perimeter of an ellipse (on plane), I know it's density function. Both ellipse equation and density are given in cartesian coordinates. So I set up a line integral, ...
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### Find the surface area of the part of the paraboloid $z=5-(x^2 + y^2)$ that lies between the planes $z=0$ and $z=1$.

I have the following math question: Find the surface area of the part of the paraboloid $z=5-(x^2 + y^2)$ that lies between the planes $z=0$ and $z=1$. So far i have computed $\sqrt{fx^2+fy^2+1}$ ...