CK-12 Geometry Concepts

http://www.ck12.org Chapter 11. Surface Area and Volume

Example C

Find the volume of the pyramid.

V=^13 ( 122 ) 12 = 576 units^3

Watch this video for help with the Examples above.

MEDIA

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CK-12 Foundation: Chapter11PyramidsB

Concept Problem Revisited

The original volume of the pyramid is^13 ( 7062 )( 407. 5 )≈ 67 , 704 , 223. 33 f t^3.

Vocabulary

Apyramidis a solid with onebaseandlateral facesthat meet at a commonvertex.The edges between the lateral

faces arelateral edges.The edges between the base and the lateral faces arebase edges.

Aregular pyramidis a pyramid where the base is a regular polygon. All regular pyramids also have aslant height,

which is the height of a lateral face.

Surface areais a two-dimensional measurement that is the total area of all surfaces that bound a solid.Volumeis a

three-dimensional measurement that is a measure of how much three-dimensional space a solid occupies.

Guided Practice

1. Find the area of the regular triangular pyramid.


2. If the lateral surface area of a square pyramid is 72f t^2 and the base edge is equal to the slant height, what is the
   length of the base edge?


3. Find the area of the regular hexagonal pyramid below.


4. Find the volume of the pyramid.


5. Find the volume of the pyramid.


6. A rectangular pyramid has a base area of 56cm^2 and a volume of 224cm^3. What is the height of the pyramid?
   Answers:


7. The area of the base isA=^14 s^2

√

3 because it is an equilateral triangle.

B=

1

4

82

√

3 = 16

√

3

SA= 16

√

3 +

1

2

( 24 )( 18 ) = 16

√

3 + 216 ≈ 243. 71