11 5 Volumes of Pyramids

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11 5Volumes of Pyramids Cones

• Objectives
• 1) Find the volume of a right Pyramid.
• 2) Find the volume of right Cone.

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I. Volume of a Pyramid

• Pyramid Is a polyhedron in which one face can
  be any polygon the other faces are triangles.

Vp ?Bh
h
Area of the Base A lw A ½bh
Height of the pyramid, not to be confused with
the slant height (l)
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Ex.1 Volume of a right Pyramid

• Find the volume of a square pyramid with base
  edges of 15cm a height of 22cm.

Square
V (?)Bh (?)lwh (?)151522 (?)4950
1650cm3
22cm
15cm
15cm
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Ex.2 Another square pyramid

• Find the area of a square pyramid w/ base edges
  16ft long a slant height 17ft.

V (?)Bh (?)lwh (?)1616___ (?)3840
1280ft3
a2 b2 c2 h2 82 172 h2 225 h 15
17ft
15
h
8ft
16ft
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II. Volume of a Cone

• Cone Is pointed like a pyramid, but its base
  is a circle.

h
Vc ?Bh
r
Area of the Base A ?r2
Height of the cone, not to be confused with the
slant height (l)
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Ex.3 Find the volume of the following right
cone w/ a diameter of 6in.
Circle
V ?Bh (?)?r2h (?)?(3)2(11) (?)99? 33?
103.7in3
11in
3in
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Ex.4 Volume of a Composite Figure
Volume of Cone first! Vc ?Bh (?)?r2h
(?)(8)2?(10) (?)(640)? 213.3? 670.2cm3
10cm
4cm
Volume of Cylinder NEXT! Vc Bh ?r2h
?(8)2(4) 256? 804.2cm3
8cm
VT Vc Vc VT 670cm3 804.2cm3 VT 1474.4cm3
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Ex.5 Solve for the missing variable.

• The following cone has a volume of 110?. What is
  its radius.

V ?Bh V ?(?r2)h 110? (?)?r2(10) 110
(?)r2(10) 11 (?)r2 33 r2 r v(33) 5.7cm
10cm
r
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What have we learned???
Height is the actual height of the solid not the
slant height!!!

• Volume of Cones Pyramids

Vc ?Bh
h
Area of Base
h
r