18-cones and pyramids

8/13/2019 18-Cones and Pyramids

1/16


2/16


3/16


4/16


5/16


6/16

The ConeA Cone is a three dimensional solidwith a circular base and a curved

surface that gradually narrows to avertex.

Volume of a Cone

=

+ + =


7/16

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


8/16

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


9/16

Cones PracticeQuestions


10/16

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


11/16

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

+ + =


12/16


13/16

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


14/16

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


15/16


16/16

Cones PracticeQuestions

18-cones and pyramids

Documents