3.1 Three-dimensional geometryIB Maths: Analysis and Approaches SL: Flashcards

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Distance between $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$?

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Distance between $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ ?: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$
Midpoint of $(1,4,-2)$ and $(5,0,6)$ ?: $(3,2,2)$
Distance from $(0,0,0)$ to $(2,3,6)$ ?: $\sqrt{4+9+36}=7$
Volume of a right pyramid?: $\frac13\times$ base area $\times$ perpendicular height
Volume of a right cone?: $\frac13\pi r^2h$
Volume and curved surface area of a hemisphere?: $V=\frac23\pi r^3$ ; curved surface $2\pi r^2$
Curved surface area of a cone?: $\pi rl$ , where $l=\sqrt{r^2+h^2}$ is the slant height
Surface area of a sphere of radius 3?: $4\pi(9)=36\pi$
In a composite solid, which faces do you leave out of the surface area?: Faces where two parts are joined, because they are hidden inside the solid.
How is the angle between a line and a plane defined?: The angle between the line and its projection onto the plane.
Length of the space diagonal of a cuboid $a\times b\times c$ ?: $\sqrt{a^2+b^2+c^2}$
Right pyramid, square base of side 10, height 12: height of a triangular face?: $\sqrt{12^2+5^2}=13$
At SL, what kind of trigonometry is set in 3D questions?: Right-angled trigonometry only (with Pythagoras).