Geometry: Circles and Solids Review

A set of vocabulary flashcards covering basic and advanced geometry concepts including area, volume, circle properties, and solid similarity.

Polyhedra

A type of solid that includes shapes such as prisms and pyramids.

Not Polyhedra

A classification for solids that includes cylinders, cones, and spheres.

Circumference of a Circle

The distance $C$ of a circle, calculated as $C = \text{π}d$ or $C = 2\text{π}r$, where $d$ is the diameter and $r$ is the radius.

Area of a Regular Polygon

The area $A$ of a regular $n$-gon with side length $s$ is one-half the product of the apothem $a$ and the perimeter $P$, expressed as $A = \frac{1}{2}aP$ or $A = \frac{1}{2}a \times ns$.

Arc Length

In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to $360^\text{∘}$, formulated as: $\text{Arc length of AB} = \frac{mAB}{360^\text{∘}} \times 2\text{π}r$.

Area of a Sector

The ratio of the area of a sector of a circle to the area of the whole circle ($\text{π}r^2$) is equal to the ratio of the measure of the intercepted arc to $360^\text{∘}$.

Area of a Circle

The area is calculated as $A = \text{π}r^2$, where $r$ is the radius of the circle.

Area of a Rhombus or Kite

The area of a rhombus or kite with diagonals $d_1$ and $d_2$ is $\frac{1}{2}d_1d_2$.

Volume of a Pyramid

The volume $V$ is calculated as $V = \frac{1}{3}Bh$, where $B$ is the area of a base and $h$ is the height.

Volume of a Prism

The volume $V$ is calculated as $V = Bh$, where $B$ is the area of a base and $h$ is the height.

Volume of a Cylinder

The volume $V$ is calculated as $V = Bh = \text{π}r^2h$, where $B$ is the area of the base and $r$ is the radius.

Volume of a Cone

The volume $V$ is calculated as $V = \frac{1}{3}Bh = \frac{1}{3}\text{π}r^2h$, where $B$ is the area of the base and $r$ is the radius.

Surface Area of a Right Cone

The surface area $S$ is given by $S = \text{π}rl$, where $r$ is the radius of the base and $l$ is the slant height.

Surface Area of a Sphere

The surface area $S$ is given by $S = 4\text{π}r^2$, where $r$ is the radius of the sphere.

Volume of a Sphere

The volume $V$ is calculated as $V = \frac{4}{3}\text{π}r^3$, where $r$ is the radius of the sphere.

Similar Solids

Two solids of the same type with equal ratios of corresponding linear measures, such as heights or radii.

Scale factor

The ratio of the corresponding linear measures of two similar solids.

Volume Ratio of Similar Solids

If two similar solids have a scale factor of $k$, then the ratio of their volumes is equal to $k^3$.

Degrees to Radians Conversion

To convert degrees to radians, multiply the degree measure by $\frac{\text{π radians}}{180^\text{∘}}$ or $\frac{2\text{π radians}}{360^\text{∘}}$.

Radians to Degrees Conversion

To convert radians to degrees, multiply the radian measure by $\frac{180^\text{∘}}{\text{π radians}}$ or $\frac{360^\text{∘}}{2\text{π radians}}$.