Volumes of Prisms & Volumes of Prisms &

CylindersCylinders

Objectives:Objectives:

1) To find the volume of a prism.1) To find the volume of a prism.

2) To find the volume of a cylinder.2) To find the volume of a cylinder.

VolumeVolume

►VolumeVolume – Is the space that a figure – Is the space that a figure occupies.occupies. Measured in cubic units.Measured in cubic units.

►cmcm33, in, in33, m, m33, ft, ft33

I. Finding the volume of a I. Finding the volume of a PrismPrism►PrismPrism – 2 congruent parallel bases, – 2 congruent parallel bases,

sides are rectangles.sides are rectangles.

Height (h)

Area of Base (B)

V = BhHeight of PrismArea of Base

A = bh (Rectangle)

A = ½bh (Triangle)

A = ½ap (Polygon)

Ex. 1: Finding the Volume of a Ex. 1: Finding the Volume of a rectangular prismrectangular prism

► The box shown is 5 The box shown is 5 units long, 3 units units long, 3 units wide, and 4 units wide, and 4 units high. How many high. How many unit cubes will fit in unit cubes will fit in the box? What is the box? What is the volume of the the volume of the box?box?

Ex.1: Find the Volume of the Ex.1: Find the Volume of the PrismPrism

5in

3in

10inV = Bh

= (3in • 5in)(10in)

= (15in2)(10in)

= 150in3

Area of Base

B = l•w

Ex.2: Find the volume of the followingEx.2: Find the volume of the following

20m

29m

40m

V = Bh

= ½bh • h

= ½(20m)__ • (40m)

= 210m2 • 40m

= 8400m3

Height of the base:

a

a2 + b2 = c2

a2 + 202 = 292

b = 21

Triangle

21

Ex.3: Yet another prism! Find Ex.3: Yet another prism! Find the the volume.volume.

8in

10in

V = Bh

= ½bh • h

= ½(8in) __ • (10in)

= (27.7in2) • (10in)

= 277in3

h = 6.9

6.9

II. Volume of a CylinderII. Volume of a Cylinder

r

h

V = Bh

Volume of right cylinder

Height of cylinder

Area of base: (Circle)

A = r2

Ex.4: Find the area of the following right Ex.4: Find the area of the following right cylinder.cylinder.

16ft

9ft

V = Bh

= r2 • h

= (8ft)2 • (9ft)

= 64ft2 • (9ft)

= 576ft3

= 1809.6ft3

Area of a Circle

Ex.5: Find the volume of the Ex.5: Find the volume of the following composite figure.following composite figure.

Half of a cylinder:

Vc = Bh

= r2•h

= (6in)2 • (4in)

= 452in3

= 452/2 = 226in3

12in

4in

11in

Volume of Prism:

Vp = Bh

= (11)(12)(4)

= 528in3

VT = Vc + Vp

= 226in3 + 528in3

= 754in3