volume of a pyramid
TRANSCRIPT
All polygons have straight sides.
Pyramid β A solid object where the base is a polygon and the sides are triangles which meet at the top
The apex is highest point.
10 m
10 m
Apex
Base
The dashed lines will indicate lines hidden by a solid polygon.
Draw lines from the four vertices to an
apex above the rhombus.
10 m
10 m
Why must you use the Pythagorean theorem?
To find the height of the pyramid.
Solve for volume
π =1
3π΅β
π2 + 52 = 132
π2 + 25 = 169
π2 = 144
π = 12
β = βπππβπ‘ ππ ππ¦πππππβ = 12 π
13 m
π΅ = 10 π β 10 π = 100 π2π΅ = π΄πππ ππ π΅ππ π
10 m
10 m
How do we proceed?
Just substitute and solve.
13 m
12 m
π =1
3100 π2 12 π
π =1
31200 π3
π = 400 π3
π =1
3π΅β
β = 12 π
π΅ = 100 π2
h=481 ft.s=756 ft.
h=heights=side of baseB= side squared
What must you do after substituting
the values? Follow the order of operations.
π =1
3571,536 ππ‘2 481 ππ‘
π =1
3756 ππ‘ 2 β 481 ππ‘
π =1
3274,908,816 ππ‘3
π = 91,636,272 ππ‘3
h=24 ms=55 m
h=heights=side of baseB= side squared
Why do mummies tell no secrets?
π =1
33,025 π2 24 π
π =1
355 π 2 β 24 π
π =1
372,600 π3
π = 24,200 π3
Because they keep things under wraps.
h=72 ft.s=112 ft.
h=heights=side of baseB= side squared
Why might you want to know the volume
of the Louvre.
π =1
312,544 ππ‘.2 72 ππ‘.
π =1
3112 ππ‘. 2 β 72 ππ‘.
π =1
3903,168 ππ‘.3
π = 301, 056 ππ‘.3
For heating and cooling purposes.
h=65 ms=225 m
h=heights=side of baseB= side squared
Who belongs to the Pyramid
PTA?
π =1
350,625 π2 65 π
π =1
3225 π 2 β 65 π
π =1
33,290,625 π3
π = 1,096,875 π3
Mummies and Deadies!
For this problem you are not give the side of
the square base, but the perimeter.
Divide the perimeter by four.
π =2,600 ππ‘
4
π = 650 ππ‘.
h=350 ft.s=650 ft.
h=heights=side of baseB= side squared
Why couldnβt the mummy answer the
phone?
π =1
3422,500 ππ‘.2 350 ππ‘.
π =1
3650 ππ‘. 2 β 350 ππ‘.
π =1
3147,875,000 ππ‘.3
π = 49,291,667ππ‘.3
She was tied up!
Review Questions
What information is not needed to find the volume?
The height of the triangle face.
What do you call the top of a pyramid?
Apex
Of corpse!Do mummies enjoy being mummies.
When give the perimeter of the base, how do you find the side of the base?
Divide the perimeter by four.
Review Questions
How do you identify a pyramid?
By the type of base.
What would you call a pyramid in which all the sides of the base are congruent with right angles?
A square pyramid
If you did not want multiply by one-third
what else could you do?
Divide by 3 1
3π΅β =
π΅β
3