query: Why is the surface area of a sphere equal to $4\pi r^2$
positive_passages.docid: 76199
positive_passages.text: Can the Surface Area of a Sphere be found without using Integration?
negative_passages.docid: 158162
negative_passages.text: Finding the volume of the tetrahedron.
negative_passages.docid: 46353
negative_passages.text: Proof that $\cos(\pi/3)=1/2$
negative_passages.docid: 67224
negative_passages.text: Why is the area under a curve the integral?
negative_passages.docid: 108909
negative_passages.text: Is the unit sphere in $\Bbb R^4$ path connected?
negative_passages.docid: 48086
negative_passages.text: Why is this series of square root of twos equal $\pi$?
negative_passages.docid: 97473
negative_passages.text: Prove that: area of triangle $S_{ABC}=p \cdot R$, where p is half perimeter of triangle $DEF$
negative_passages.docid: 58953
negative_passages.text: Area of intersection between 4 circles centered at the vertices of a square
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: 84189
negative_passages.text: Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
negative_passages.docid: 95145
negative_passages.text: Does $\exp(2ir\pi)$ equal $1$? What's wrong?
negative_passages.docid: 82309
negative_passages.text: Volume of a solid created by an extended tetrahedron
negative_passages.docid: 149352
negative_passages.text: What is the Riemann surface of $y=\sqrt{z+z^2+z^4+\cdots +z^{2^n}+\cdots}$?
negative_passages.docid: 41550
negative_passages.text: Find the Area of the ellipse
negative_passages.docid: 14234
negative_passages.text: Q: Volume involving spherical and polar coordinates
negative_passages.docid: 75731
negative_passages.text: Significance of $\pi$ in physics
negative_passages.docid: 6151
negative_passages.text: Evaluating $\int_a^b \frac12 r^2\ \mathrm d\theta$ to find the area of an ellipse