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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