IB Maths AI 3.1 Definitions

A solid with a circular base and a curved surface meeting at a single vertex; for a right cone, $V=\frac{1}{3}\pi r^2h$ where $r$ is the base radius and $h$ is the perpendicular height.

$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}$.

Half of a sphere cut by a plane through its centre; its volume is $V=\frac{2}{3}\pi r^3$.

The point halfway along the line segment joining two points; for $A\left(x_1,y_1,z_1\right)$ and $B\left(x_2,y_2,z_2\right)$ it is $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)$.

A solid with a polygon base and triangular faces that meet at a single vertex; for a right pyramid, $V=\frac{1}{3}Ah$ where $A$ is the base area and $h$ is the perpendicular height.

A pyramid whose apex is vertically above the centre of its base; its volume is $V=\frac{1}{3}Ah$, where $A$ is the base area and $h$ is the perpendicular height.

A solid consisting of all points at a fixed distance $r$ from a centre; its volume is $V=\frac{4}{3}\pi r^3$.

A measure of how much space a three-dimensional solid occupies, usually expressed in cubic units such as cm³.