13.1 Volumes of Prisms and CylindersPresented by Christina

Thomas and Kyleelee

Objectives• Find volumes of prisms (right &

oblique)• Find volumes of cylinders (right &

oblique)

Now THAT’S what I call volume….

Definition of Volume• The volume of a figure is the measure

of the amount of space that figure encloses.

• Volume is measured in cubic units.Instead of measuring each square on the surface, we measure each cube that makes up the figure.

• If a prism has a volume of V cubic units, a height of h units, and each base has an area of B square units, then V=Bh.

Or B= area of baseB=

Or V=Bh

Example 1 You want to share this delicious

piece of chocolate with your friend. Find the volume of half the Toblerone bar, or the right triangular prism, to the nearest tenth.

The ‘WORK’

First find length of base of prisma2 + b2 = c2

a2 + 92 =112

a2 + 81 =121a2 = 40a = 6.3Next find volume of prismV = BhV = .5(9)(6.3)(17)V = approx. 482 cm3

Pythagorean Theoremb=9, c=11MultiplySubtract 81 from each sideTake the square root of each side

Volume of a prismB = .5(9)(6.3), h = 17Simplify

• Like the volume of a prism, volume of a cylinder is the product of the area of the base and the height.

• If a cylinder has a volume of V cubic units, then it has a height of h units, and the bases have radii of r units, then V = Bh or V= r2h

Example 2 Find the

volume of this gigantic can of Campbell soup.

h

The ‘WORK’First find the height a2 + b2= c2 h2 + 62 = 142

h2 + 36 = 196h2 = 160h = 12.6Now find volume of cylinderV = r2hV = (32 ) (12.6)V = approx. 356.3 in3

Pythagorean Theorema = h, b = 6, and c = 14MultiplySubtract 36 from each sideTake the square root of each side

Volume of Cylinderr = 3 and h = 12.6Simplify

Do oblique and right solids have the same volume?

• The best way to understand this is to look at a stack of CDs. Since each stack has the same number of CDs, with each CD the same size and shape, the two prisms must have the same volume.

If all parts of the solids used in the formula stay the same, then you will get the same answer.

This is also known as…Cavalieri’s PrincipleIf two solids have

the same height and the same cross-sectional area at every level, then they have the same volume.

This means that if a solid has a base with an area of B square units and a height of h units. Then its volume is Bh cubic units, whether it is right or oblique.

Example 3Find the volume of this oblique rectangular prism.

(One of the leaning towers of Madrid)

The ‘WORK’V= Bh

V= (22)(19)(78)

V= 32, 604 ft3

Volume of a rectangular prism

B = l x w, l = 22, w = 19, h = 78Simplify

Pg. 692-693 #7-24, 26, 28

Good luck ;)