query: Calculate the volume bounded by the surface $(x^2+y^2+z^2)^2 = x$
positive_passages.docid: 20481
positive_passages.text: Volume enclosed by $(x^2+y^2+z^2)^2=x$
negative_passages.docid: 117291
negative_passages.text: Deriving formula for surface area of an ellipsoid
negative_passages.docid: 30246
negative_passages.text: Find the equation of the tangent plane to the surface $x^{\frac{2}{3}}+y^{\frac{2}{3}}+z^{\frac{2}{3}}=2^{\frac{2}{3}}$ at $(x_0,y_0,z_0)$
negative_passages.docid: 100189
negative_passages.text: What is the maximum volume of a cylinder that can fit in a sphere of a constant radius?
negative_passages.docid: 33105
negative_passages.text: Find the value of $a^2-b^2+c^2$
negative_passages.docid: 15604
negative_passages.text: Determine the set of points $z$ that satisfy the condition $|2z|>|1+z^2|$
negative_passages.docid: 63726
negative_passages.text: Surface area of sphere $x^2 + y^2 + z^2 = a^2$ cut by cylinder $x^2 + y^2 = ay$, $a>0$
negative_passages.docid: 95004
negative_passages.text: Infinite Volume but Finite Surface Area
negative_passages.docid: 27911
negative_passages.text: How can I prove that $xy\leq x^2+y^2$?
negative_passages.docid: 13572
negative_passages.text: $x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
negative_passages.docid: 26259
negative_passages.text: Get surface area of a mesh?
negative_passages.docid: 62209
negative_passages.text: Finding multivariable limits for the function $\frac{3x^2y}{x^2+y^2}$
negative_passages.docid: 11875
negative_passages.text: how to calculate the bounding square of an ellipse?
negative_passages.docid: 61585
negative_passages.text: Why is area of a surface of revolution integral $2\pi y~ds$? not '$dx$'?
negative_passages.docid: 44998
negative_passages.text: Compute integral closure of $F[x,y,z]/(x^2-y^2z)$.
negative_passages.docid: 103416
negative_passages.text: Proving area under curve
negative_passages.docid: 49946
negative_passages.text: A determinant coming out from the computation of a volume form