Geometry Honors - 3-Dimensional and Solid Geometry

These flashcards cover key vocabulary terms related to 3-dimensional geometry including definitions and important concepts.

Volume of a Prism

The volume is calculated as V = B * H, where B is the base area and H is the height.

Surface Area of a Cylinder

The surface area consists of the lateral area and the area of the bases, calculated as S = 2πrh + 2πr².

Volume of a Sphere

The volume is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

Euler's Formula for Polyhedra

For any convex polyhedron, the relationship between vertices (V), edges (E), and faces (F) is given by V - E + F = 2.

Dihedral Angle

A three-dimensional angle formed between two intersecting planes.

What is the formula for the volume of a tetrahedron?

The volume $V$ of a tetrahedron is given by the formula $V = \frac{1}{3} A{base} h$, where $A{base}$ is the area of the base and $h$ is the height.

What is Euler's formula for polyhedra?

Euler's formula states that for any convex polyhedron, the relationship between the number of vertices $V$, edges $E$, and faces $F$ is $V - E + F = 2$.

What is the formula for the surface area of a cube?

The surface area $A$ of a cube with side length $s$ is given by $A = 6s^2$.

What is the formula for the volume of a rectangular prism?

The volume $V$ of a rectangular prism is given by the formula $V = l \cdot w \cdot h$, where $l$ is the length, $w$ is the width, and $h$ is the height.

What is the formula for the surface area of a sphere?

The surface area $A$ of a sphere is given by the formula $A = 4 \pi r^2$, where $r$ is the radius.

What is the formula for the volume of a cylinder?

The volume $V$ of a cylinder is given by the formula $V = \pi r^2 h$, where $r$ is the radius of the base and $h$ is the height.

What is the formula for the volume of a cone?

The volume $V$ of a cone is given by the formula $V = \frac{1}{3} \pi r^2 h$, where $r$ is the radius of the base and $h$ is the height.

What is the formula for the surface area of a cone?

The surface area $A$ of a cone is given by the formula $A = \pi r (r + l)$, where $r$ is the radius of the base and $l$ is the slant height.