𝐒𝐎𝐋𝐈𝐃𝐒 ˃ᴗ˂

formulas + definitions + principles !!

LA = ½ P*l*, where P is the perimeter of the base and *l* is the slant height.

lateral area of a pyramid

SA=LA+B, where B is the area of the base of the pyramid.

surface area of a pyramid

V= ⅓ Bh, where B is the area of the base and h is the height of the pyramid.

volume of a pyramid

A cylinder is a solid that has two parallel congruent bases and a rounded lateral surface.

definition of cylinder

 la = 2πrh

lateral area of a cylinder

 sa = 2πrh +  2πr^2

surface area of a cylinder

v = πr^2h

volume of a cylinder

cone is a solid that has a single circular base and a single lateral surface that ends at a point (apex).

def of cone

la = πrl

lateral area of cone

sa = πrl + πr^2

surface area of cone

v = 1/3πr^2h

volume area of cone

A solid that is the set of all points a fixed distance away from a fixed point in space.

def of sphere

SA = 4πr^2

surface area of sphere

v = 4/3πr^3

volume of sphere

v = 2/3πr^3

volume of hemisphere

plane (determined by 3 points)

Basic “unit” in 3-D space

plane

There is one and only one \[BLANK\] containing three non-collinear points.

one

There is exactly \[BLANK\] plane containing a line and a point not on the line.

intersect

If two lines \[BLANK\], then there exists exactly one plane containing them.

parallel

There is exactly one plane containing two distinct \[BLANK\] lines.

Parallel lines in space are lines in the same plane that have no points in common.

What does it mean for two lines to be parallel in space?

one

If two planes intersect, then they intersect at exactly \[BLANK\] line.

parallel

If a plane intersects two parallel planes, then the intersection is…?

parallel

Two planes are perpendicular to the same line if and only if the planes are…?

The **lateral area** (of a prism) is the area of all sides of the prism, excluding the area of its bases. 

**E.g.** The lateral area of a cube is the area of four of the sides.

def of lateral area

A __right prism__ has its lateral faces perpendicular to the base.

def of right prism

LA = Ph

* P is the perimeter of one of the bases
* h is the height of the prism

general lateral area formula

SA = LA+2B

* LA is the lateral area of the prism
* B is the area of one of the prism’s bases

general surface area formula

tells us that if 2 figures have the same height and the same cross-sectional area at every point along that height, they have the same volume

Cavalieri's principle