Volumes of Prisms &amp; Cylinders

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# Volumes of Prisms &amp; Cylinders - PowerPoint PPT Presentation

Volumes of Prisms &amp; Cylinders. Objectives: 1) To find the volume of a prism. 2) To find the volume of a cylinder. Volume. Volume – Is the space that a figure occupies. Measured in cubic units. cm 3 , in 3 , m 3 , ft 3. I. Finding the volume of a Prism.

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### Volumes of Prisms & Cylinders

Objectives:

1) To find the volume of a prism.

2) To find the volume of a cylinder.

Volume

Volume – Is the space that a figure occupies.

Measured in cubic units.

cm3, in3, m3, ft3

I. Finding the volume of a Prism

Prism – 2 congruent parallel bases, sides are rectangles.

V = Bh

Height of Prism

Area of Base

A = bh (Rectangle)

A = ½bh (Triangle)

A = ½ap (Polygon)

Height (h)

Area of Base (B)

The box shown is 5 units long, 3 units wide, and 4 units high. How many unit cubes will fit in the box? What is the volume of the box?Ex. 1: Finding the Volume of a rectangular prism
Ex.1: Find the Volume of the Prism

Area of Base

B = l•w

V = Bh

= (3in • 5in)(10in)

= (15in2)(10in)

= 150in3

10in

3in

5in

Ex.2: Find the volume of the following

Triangle

29m

V = Bh

= ½bh • h

= ½(20m)__ • (40m)

= 210m2 • 40m

= 8400m3

a

40m

21

20m

Height of the base:

a2 + b2 = c2

a2 + 202 = 292

b = 21

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

h = 6.9

10in

V = Bh

= ½bh • h

= ½(8in) __ • (10in)

= (27.7in2) • (10in)

= 277in3

8in

6.9

II. Volume of a Cylinder

Height of cylinder

r

V = Bh

h

Volume of right cylinder

Area of base: (Circle)

A = r2

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

Area of a Circle

V = Bh

= r2• h

= (8ft)2 • (9ft)

= 64ft2 • (9ft)

= 576ft3

= 1809.6ft3

16ft

9ft

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

Half of a cylinder:

Vc = Bh

= r2•h

= (6in)2 • (4in)

= 452in3

= 452/2 = 226in3

11in

4in

Volume of Prism:

Vp = Bh

= (11)(12)(4)

= 528in3

12in

VT = Vc + Vp

= 226in3 + 528in3

= 754in3