Volumes of Pyramids & Volumes of Pyramids & ConesCones

Objectives:Objectives:

1) Find the volume of a 1) Find the volume of a right right Pyramid.Pyramid.

2) Find the volume of 2) Find the volume of right right Cone.Cone.

I. Volume of a PyramidI. Volume of a Pyramid

PyramidPyramid – Is a polyhedron in which one – Is a polyhedron in which one face can be any polygon & the other faces face can be any polygon & the other faces are triangles.are triangles.

hVVpp = = ⅓Bh⅓Bh

Area of the Base

A = l•w

A = ½bh

Height of the pyramid, not to be confused with the slant height (l)

Ex.1: Volume of a right PyramidEx.1: Volume of a right Pyramid

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

22cm

15cm

15cm

V = (⅓)Bh

= (⅓)l•w•h

= (⅓)15•15•22

= (⅓)4950

= 1650cm3

Square

II. Volume of a ConeII. Volume of a Cone

ConeCone – Is “pointed” like a pyramid, but its – Is “pointed” like a pyramid, but its base is a circle.base is a circle.

h

r

VVcc = = ⅓Bh⅓Bh

Area of the Base

A = r2Height of the cone, not to be confused with the slant height (l)

Ex.3: Find the volume of the following Ex.3: Find the volume of the following right cone w/ a diameter of 6in.right cone w/ a diameter of 6in.

11in V = ⅓Bh

= (⅓)r2h

= (⅓)(3)2(11)

= (⅓)99

= 33 = 103.7in3

Circle

3in

Ex.5: Solve for the missing variable.Ex.5: Solve for the missing variable.The following cone has a volume of 110The following cone has a volume of 110. .

What is its radius. What is its radius.

10cm

r

V = ⅓Bh

V = ⅓(r2)h

110 = (⅓)r2(10)

110 = (⅓)r2(10)

11 = (⅓)r2

33 = r2

r = √(33) = 5.7cm

Ex.4: Volume of a Composite FigureEx.4: Volume of a Composite Figure

8cm8cm

10cm10cm

4cm4cm

Volume of Cone first!

Vc = ⅓Bh

= (⅓)r2h

= (⅓)(8)2(10)

= (⅓)(640)

= 213.3 = 670.2cm3

Volume of Cylinder NEXT!

Vc = Bh

= r2h

= (8)2(4)

= 256 = 804.2cm3

VT = Vc + Vc

VT = 670cm3 + 804.2cm3

VT = 1474.4cm3