Lesson 13.1-Volume of Prisms and Cylinders
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Lesson 13.1-Volume of Prisms and Cylinders. Objectives. Find volumes of prisms Find volumes of cylinders. Definition of Volume. Volume is a measure of the amount of space that a figure encloses Volume is always recorded in cubic units ex. cm. 3

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Lesson 13.1-Volume of Prisms and Cylinders

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Lesson 13 1 volume of prisms and cylinders

Lesson 13.1-Volume of Prisms and Cylinders


Objectives

Objectives

Find volumes of prisms

Find volumes of cylinders


Definition of volume

Definition of Volume

Volume is a measure of the amount of space that a figure encloses

Volume is always recorded in cubic units ex. cm.3

Remember that if there is a part cut out of the center of the figure you have to subtract it’s volume from the volume of the entire figure


Base height

Base Height

  • To find the volume of a prism use the formula V=Bh

    V=Volume

    B=Area of the base

    h=height of prism


Example 1

Example #1

Find the

volume of

this figure

10ft. 12 ft. 13ft.


Lesson 13 1 volume of prisms and cylinders

10ft. 12ft. 13ft.

13ft.

x

5ft.

1)Find the area of the triangular base

2)Create the height of one of the bases and use Pythagorean Theorem to find the height of the base.

3)132=52+x2

4) x2= 144

5) h= 12

6)Find area of triangular base,

A=1/2(10)(12)

A=(5)(12)

A=60ft.2

7)V=Bh

V=(60)(12) V=720ft.3


Volume of cylinders

Volume of Cylinders

To find the volume of a cylinder, use

V=πr²h

This is basically the area of

height of the base times the height just like

in a prism

radius


Example 2

Example #2

24m.

1)Take ½ of the diameter to get the radius.

2)1/2 of the diameter is twelve, now plug everything into the formula

3)V= π(122)(30)

4) V=(144)(π)(30)

5)V=4320π or 13,571.7m.3

30m.


Example 3

Example #3

  • Sometimes it gives you the diagonal of the cylinder and you have to use the Pythagorean Theorem to find the height.

  • 102 = 62+x2

  • X2=64

  • X=8ft.

  • Now plug everything into the formula

  • V=32π(8)

  • V=9π8

  • V=72π or 226.2 ft.3

10 ft.

6 ft.

x


Cavalieri s principle

Cavalieri’s Principle

1) If two solids have the same height and the same cross-sectional area at every level, then they have the same volume…….


Example 4

Example #4

  • Sometimes the cylinder is not a right cylinder and the height will be outside the cylinder.

  • Use the same formula using the height that is outside the cylinder.

  • V=42π(9)

  • V=16π(9)

  • V=144π or 452.4 yds.3

9 yd.

4 yd.


Assignment

Assignment

P.692

#7-16, #18, #22-23

Bonus-#28


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