h.geometry chapter 10 definition sheet · *** formula applies to regular pyramids and right...

H.Geometry – Chapter 10 – Definition Sheet

___

RECALL:

_________________________

_________________________

- Measure of the boundary of a 3-D figure (the area of the ____________) - The measure of the space enclosed by a 3-D figure.

Sketch a net for a box with base edges of 7 cm. and 20 cm. and the height is 15 cm.

Nets for Right Prism and Right Cylinder Nets for Regular Pyramid

Section 10.1.5


Definition of :

Surface Area

Lateral Area

___________________________________________________________________ ___________________________________________________________________

Lateral Area Formula for right

prisms/cylinders

_____________________________________ Where: H = ____________________________ P = ____________________________ ____________________________

*** Applies only to _________________ prisms or cylinders. ***

Surface Area Formula for

prisms/cylinders

_____________________________________ Where: LA = ________________________________ B = _________________________________

***Applies to ____________ prism or cylinder*** NOTE: Total surface are adds the area of the 2 __________ to the LA

Lateral Area Formula for

Regular pyramids/right cones

_______________________________________ Where: _____ = slant height of the regular pyramid/right cone P = _____________________________________ _____________________________________

*** Formula applies to regular pyramids and right cones***


Surface Area Formulas for

pyramids/cones

________________________________________ Where: LA = ______________________________________ B =_______________________________________ *** Formula applies to ___________ pyramid or cone.***

*** Total surface area adds the base area to the ____________________ area.***


Re ___________________________ ___________________________

-The total area of all the faces or surfaces of a solid. - Measured in square units - The measure of the amount of space contained in a solid. - Measured in cubic units Ex. Cubic centimeters or _____________________ Cubic inches or __________________________ Cubic feet or ____________________________ Cubic meters or _________________________

Section 10.2


Volume of any

_____________________

Or

_________________

__________________________________________

Volume of

_____________________

Or

_________________

__________________________________________


Prism – Cylinder Volume

Formula

__________________________________________ Where: V = ____________________________________ B = ____________________________________ H = ____________________________________

*** Works for both _____________ and_________________***

(1) 5 cm.

9 cm.


If bases are _________________________ and the heights are equal, what is the relationship between the volumes of: Prisms and Pyramids?______________________________________________________________________________ ______________________________________________________________________________ Cylinders and Cones? ______________________________________________________________________________ ______________________________________________________________________________

Pyramid – Cone Volume

Formula

_______________________ or _____________________________ Where: V = _____________________________________________ B = ______________________________________________ H = ______________________________________________

*** Because of Cavalieri’s principle, it works for right and oblique pyramids and cones. ****

Section 10.3


Definition of:

Displacement

-The volume of water moved (___________________________) by an _______________________________ in the water -The volume of the object equals the _____________________________________ ___________________________________________________

***Thus, the volume of the object is related to the __________________________ ____________________________________________________________________

Displacement Formula

-Volume of an object submerged in water

𝑉𝑜𝑏𝑗𝑒𝑐𝑡= ________________________________________

Where: B = ______________________________ ∆H = ______________________________

Section 10.5


Density

______________________________________________________________

- A denser object will have more weight in a smaller volume of space.

- Typical Units: ___________, ___________, ___________, ___________ Density Formula: _____________________________________ Note: compounds have a specific density! Thus an unknown compound can be identified by its’ density. (see Table!)

Example: A chunk of rock is places in a cylindrical container whose radius is 2 cm. Then the rock is fully submerged, the water level in the container rises 1.4 cm.

(a) Find the volume of the rock.

(b) The mass of the rock is 158 grans, Find its’ density.

(c) Using the density chart, identify the rock’s content.


Section 10.6

Section 7.5


****Deriving the formula for the surface area of a sphere (Investigation, pg.562)************

Step 1: Divide the surface of the sphere into m “polygons,” each with area of B. Therefore: Surface Area of Sphere: SA = ________________________________________ Step 2: Each “polygon” is the base of a “pyramid” with it’s vertex at the sphere’s center _______________________________________________________________________ Therefore:

𝑉𝑠𝑝ℎ𝑒𝑟𝑒 = 𝑆𝑢𝑚 𝑜𝑓 𝑉𝑜𝑙𝑢𝑚𝑒𝑠 𝑜𝑓 𝑃𝑦𝑟𝑎𝑚𝑖𝑑𝑠

or _______=______________________________

so: _______________________________________________________ _______________________

Section 10.7

Section 7.5


Sphere Surface Area Formula: ________________________________

Where: SA = ________________________ r = ________________________

Examples: Find the surface area of:

(a). (b). (c). (d). A sphere has surface are of 576π 𝑐𝑚2. Find the volume of the sphere. (e). The volume of a sphere is 4500π 𝑐𝑚3. What is the sphere’s surface area?

6 in.

18 cm

10 cm.


Triangles

Triangles

Note: In a right triangle, if the shorter

leg is half the length of the

hypotenuse, it’s a 30-60-90 right

triangle.


A

C

B

h.geometry chapter 10 definition sheet · *** formula applies to regular pyramids and right...

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