Aim: The Third Dimension: Volume

1
Aim The Third Dimension Volume What is it?
Do Now What is the area, in terms of p, of the
shaded region in the figure below?
s
A. of sq. s2
A. of circle pr2

1. of shaded region A. of sq. - A. of circle

A. of s. r. s2 - p (1/2s)2
s2 - p (1/4 s2)
s2 - 1/4s2 p
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Perimeter Area
Perimeter - the distance around a polygon
P 1 2 3 4
Area - the space inside a polygon - measured in
square units
units2, in2, miles2, etc.
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Volume
Volume - the measure of the space inside a
polyhedron -measured in cubic units.
8 cubic units.
V Bh, where B the area of the base
27cubic units.
Polyhedron - three dimensional figure whose
surfaces are polygons
Edge a segment that is the intersection of two
faces
Vertex point where edges meet
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Volume Formulas
Prism a polyhedron with two congruent, parallel
bases. The other faces are lateral faces.
Prism
B - area of the base
h
w
l
b
Rectangular B l w
Triangular B 1/2 bh
Rectagular prism V l ? w ? h
A triangular prism is a solid whose base is a
triangle.
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Model Problems
10
Find the Volume of the following polyhedron
13
17
V l w h 17 x 13 x 10
2210 units3
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Model Problem
What is the volume of a rectangular box whose
base measures 3 units by 10 units and whose
height is 20 units?
Rectangular prism V l ? w ? h
V 10 ? 3 ? 20 600 units3
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Model Problem
The volume of a rectangular box is 2,400 cu.
units. The measurements of the base are 60 x
20. What is the height of the box?
2400 units2
h
20
w
60
l
2400 60 x 20 x h
2400 1200 x h
2 h
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Model Problem
The base of a triangular prism has an area of 15
cm2 and a height of 30 cm. What is the volume of
the triangular prism?
Triangular prism V B ? h
V 15cm2 ? 30 450 units3
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Volume Formula
Prism a polyhedron with two congruent, parallel
bases. The other faces are lateral faces.
What is the volume of a cube with a side of 10
units?
10
Volume Formulas
11
Model Problems
A cylindrical tank has a radius of 10 ft. and a
height of 25 ft. What is its volume? Give your
answer in terms of ?
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Volume Formulas
Pyramid 3 dimensional figure with a single base
and sides that are triangles.
13
Model Problems
B l w
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Volume Formula
Cone
Cone a pyramid with a circle for a base
What is the volume of a cone whose height is 10
units and whose base has radius 5? Express in
terms of ?
 
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Model Problems
The main tank at the Living Seas Aquarium at
EPCOT Center in Florida is the largest enclosed
tank in the world. It is a cylinder with
diameter 203 ft. and height 25 ft. About how
many million gallons of water does this tank
hold? (1 gal. 231 in3 1728 in3 1 ft3)
203 ft.
25 ft.
Radius is 1/2 the diameter r 203 ? 2 101.5
ft.
h 25
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Model Problems
The Great Pyramid at Giza, Egypt, was built about
2580 B.C. as a final resting place for Pharoah
Khufu. At the time it was built, its height was
about 481 ft. Each edge of the square base was
756 feet long.
A. Find the surface area of the
Great Pyramid, including its
base.
Height 481 ft.
756
756 ft
B. Find the volume of the Great Pyramid.
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Model Problems
Zia is planning to landscape her backyard.
The yard is a 70ft-by-60ft rectangle. She plans
to put down a 4- in. layer of topsoil. She can
buy bags of topsoil at 2.50 per 3-ft3 bag, with
free delivery. Or she can buy bulk topsoil for
25.00 per yd3, plus a 20 delivery fee. Which
option is less expensive. Show your calculations
and explanation. (1 yd3 9 ft3)
60
4

70 feet
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Model Problems
A cylinder has be cut out of the figure below.
Find the volume of the remaining figure. Round
your answer to the nearest tenth.
4
6 in.
6 in.
6 in.
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Volume Formulas
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Volume Formulas