18-Cones and Pyramids
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Transcript of 18-Cones and Pyramids
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The ConeA Cone is a three dimensional solidwith a circular base and a curved
surface that gradually narrows to avertex.
Volume of a Cone
=
+ + =
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Find the volume of a cylinder with a radiusr=1 m and height h=2 m. Find the volumeof a cone with a radius r=1 m and height
h=1 m
Volume of a Cylinder= base x height= r 2h
= 3.14(1) 2 (2)
= 6.28 m 3
Exercise #1
Volume of a Cone =(1/3) r 2h
= (1/3)(3.14)(1)2
(2)= 2.09 m 3
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Find the area of a cone with aradius r=3 m and height h=4 m.
Use the PythagoreanTheorem to find l
l 2 = r2 + h2l 2 = (3) 2 + (4) 2
l 2 = 25
l = 5
Surface Areaof a Cone
Surface Area of a Cone
= r 2 + rl
= 3.14(3) 2 + 3.14(3)(5)
= 75.36 m 2
r = the radius h = the height l = the slant height
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Cones PracticeQuestions
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A Pyramid is a three dimensional figure with aregular polygon as its base and lateral facesare identical isosceles triangles meeting at a
point.
Pyramids
base = quadrilateral base = pentagon base = heptagon
Identical isoscelestriangles
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Volume of a Pyramid: V = (1/3) Area of the base x heightV = (1/3) Ah
Volume of a Pyramid = 1/3 x Volume of a Prism
Volume of Pyramids
+ + =
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Surface Area= area of base+ 5 (area of one lateral face)
Area of Pyramids
Find the surface area of thepyramid.height h = 8 m apothem a = 4 m side s = 6 m
h
as
Area of a pentagonl
What shape is the base?
= Pa= (5)(6)(4)= 60 m2
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Area of Pyramids
Find the surface area of thepyramid.height h = 8 m apothem a = 4 m side s = 6 m
h
as
Area of a triangle= base (height)
l
What shape are the lateral sides?
l 2 = h2 + a2 = 82 + 42 = 80 m2
l = 8.9 m
Attention! the height of thetriangle is the slant height l
= (6)(8.9)= 26.7 m2
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Cones PracticeQuestions