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

Finding the volume of a Finding the volume of a PrismPrism►PrismPrism – 2 – 2 parallel bases and faces parallel bases and faces

are rectangles. Cross sections are are rectangles. Cross sections are congruent to the bases. What is a congruent to the bases. What is a Cross section?

Height (h)

Area of Base (B)

V = BhHeight of PrismArea of Base or

Cross Section

A = lw (Rectangle)

Finding the Volume of a 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?

Find the Volume of the PrismFind the Volume of the Prism

5in3in

10inV = Bh

= (3in • 5in)(10in)

= (15in2)(10in)

= 150in3

Area of Base

B = l•w

Discussion: What prism is this? Discussion: What prism is this? Look at the Look at the Cross Section to to determine. Why can’t you use l • determine. Why can’t you use l • w • h?w • h?

8in

10inV = Bh

= ½bh • h

= ½(8in) __ • (10in)

= (12in2) • (10in)

= 120in3

3in

3 in

Now work on this prism! It’s tricky so Now work on this prism! It’s tricky so be careful.be careful.

20m

29m

40m

V = Bh

= ½bh • h

= ½(20m)__ • (40m)

= 210m2 • 40m

= 8400m3Height of the base:

a

a2 + b2 = c2

a2 + 202 = 292

a = 21

Triangle

21

Volume of a CylinderVolume of a CylinderVideo for help: Video for help: YouTube

r

h

V = Bh

Volume of right cylinder

Height of cylinder

Area of base or cross section: (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

= 3.14(8ft)2 • (9ft)

= 200.96ft2 • (9ft)

= 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

12in4in

11in

Volume of Prism:

Vp = Bh

= (11)(12)(4)

= 528in3

VT = Vc + Vp

= 226in3 + 528in3

= 754in3

What have we learned??What have we learned??Volume of a prism or a cylinder:

V = Bh

Capitol “B” stands for area of the base.

Composite Figures: Made up of two separate solids.