A way to describe or model the “closeness” of items in a particular situation It is the spatial property of being “crowded” together (c) copyright 2014

Propensity for Density

What is density?• A way to describe or model the “closeness” of items in a particular situation• It is the spatial property of being “crowded” together

(c) copyright 2014 - all rights reserved www.cpalms.org

How do you calculate density?

• It is a ratio that compares the measure of how much of a certain item is packed into a defined unit of area or volume• It is (the number of things in an item) (the size of the item)


One equation for density is:

Where D is density, m is mass, and V is volume

(You may have used this in a science course)


This equation can be written in various forms:


Think about density in general as:

the amount of something of interest per unit size where size is an area in 2-dimensions or

a volume in 3-dimensions


Equations:2-dimensions

3-dimensions


Formulas for area:Rectangle A = bhSquare A = s2

Parallelogram A = bhTriangle A = ½ bhTrapezoid A = ½ h(b1 + b2)

Circle A = r2

Regular Polygon A = ½ aP


Formulas for volume:Rectangular Prism V = bwh = BhCube V = s3

Right Circular CylinderV = r2h = BhRight Square Pyramid V = 1/3 BhRight Circular Cone V = 1/3 r2h = 1/3 BhSphere V = 4/3 r3


Problem 1:a. Which cubic unit has the highest density of

smiley faces? b. Which cubic unit has the lowest density of smiley

faces?

A. B. C. D.


Problem 1:a. Which cubic unit has the highest density of

smiley faces? b. Which cubic unit has the lowest density of smiley

faces? A. B. C. D.

highest

lowest


Problem 2:a. Which array has the highest density of shaded cells? b. Which array has the lowest density of shaded cells?

A. B. C. D.


Problem 2:a. Which array has the highest density of shaded cells? b. Which array has the lowest density of shaded cells?

A. B. C. D.

highes

tlowest


Problem 3:a. Which hexagon interior has the highest density of un-shaded circles? b. Which hexagon interior has the lowest density of un-shaded circles?

A. B. C. D.


Problem 3:a. Which hexagon interior has the highest density of un-shaded circles? b. Which hexagon interior has the lowest density of un-shaded circles?

A. B. C. D.

highest

lowest


Problem 4:.

a. Which total cylinder has the highest density of stars? b. Which total cylinder has the lowest density of stars? A. B. C. D.


Problem 4:.

a. Which total cylinder has the highest density of stars? b. Which total cylinder has the lowest density of stars? A. B. C. D.

highest

lowest(c) copyright 2014 - all rights reserved www.cpalms.org

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A way to describe or model the “closeness” of items in a particular situation It is the spatial property of being “crowded” together (c) copyright 2014