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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
H.Geometry – Chapter 10 – Definition Sheet
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***
H.Geometry – Chapter 10 – Definition Sheet
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.***
H.Geometry – Chapter 10 – Definition Sheet
H.Geometry – Chapter 10 – Definition Sheet
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
H.Geometry – Chapter 10 – Definition Sheet
Volume of any
_____________________
Or
_________________
__________________________________________
Volume of
_____________________
Or
_________________
__________________________________________
H.Geometry – Chapter 10 – Definition Sheet
Prism – Cylinder Volume
Formula
__________________________________________ Where: V = ____________________________________ B = ____________________________________ H = ____________________________________
*** Works for both _____________ and_________________***
(1) 5 cm.
9 cm.
H.Geometry – Chapter 10 – Definition Sheet
H.Geometry – Chapter 10 – Definition Sheet
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
H.Geometry – Chapter 10 – Definition Sheet
H.Geometry – Chapter 10 – Definition Sheet
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
H.Geometry – Chapter 10 – Definition Sheet
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.
H.Geometry – Chapter 10 – Definition Sheet
Section 10.6
Section 7.5
H.Geometry – Chapter 10 – Definition Sheet
H.Geometry – Chapter 10 – Definition Sheet
****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
H.Geometry – Chapter 10 – Definition Sheet
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.
H.Geometry – Chapter 10 – Definition Sheet
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.
H.Geometry – Chapter 10 – Definition Sheet
A
C
B