enVision Geometry- Chapter 11 Notes

Apothem

the distance from the center of a regular polygon to any side

Radius

the distance from the center of a regular polygon to its vertex

Composite figure

a figure that's made up of separate basic figures (regions)

Cavalieri's Principle

If 2 or more 3D figures have the same height and same cross-sectional area at every point/level, then they have the same volume.

1 gallon= ...in³

231

The the largest cross-section of a circle is known as...

the Great Circle

Composite solid

a figure that is made of multiple shapes

Surface area is a^? times of the original

a²

Volume is a^? times of the original

a³

Area formula for regular polygon

A= 1/2 (ap)

Volume formula for rectangular prism

V= LWH

Surface area formula for rectangular prism

SA= 2LW + 2LH + 2WH

Volume formula of non-rectangular prism

V= Bh

Surface area formula of non-rectangular prism

SA= hp + 2B

Volume formula for cylinder

V= πr²h

Surface area formula for cylinder

SA= 2πr² + 2πrh

Volume formula for pyramid

V= 1/3 (Bh)

Volume formula for cone

V= 1/3 (πr²)h

Volume formula for sphere

V= 4/3 (πr³)

Surface area formula for sphere

SA= 4πr²

Volume formula for hemisphere

V= 2/3 (πr³)

Surface area for hemisphere

SA= 2πr² + πr² or SA= 3πr²

SOH CAH TOA

Sine: Opposite, Hypotenuse-- Cosine: Adjacent, Hypotenuse-- Tangent: Opposite, Adjacent

Pythagorean Theorem

a² + b² = c²