Geometry Surface Area of Prisms and Cylinders

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Geometry Surface Area of Prisms and Cylinders
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Warm Up
Draw the top, left, and right views of each
object. Assume there are no hidden cubes.
b.
c.
a.
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Surface Area of Prisms and Cylinders
Prisms and cylinders have 2 congruent parallel
bases. A lateral face is not a base. The edges of
the base are called base edges. A lateral edge is
not an edges of a base. The lateral faces of a
right prism are all rectangles. An oblique prism
has at least one nonrectangular lateral face.
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An altitude of a prism or cylinder is a
perpendicular segment joining the planes of the
bases. The height of a three-dimensional figure
is the length of an altitude. Surface area is
the total area of all faces and curved surfaces
of a three-dimensional figure. The lateral area
of a prism is the sum of the areas of the lateral
faces.
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The net of a right prism can be drawn so that the
lateral faces form a rectangle with the same
height as the prism. The base of the rectangle is
equal to the perimeter of the base of the prism.
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Lateral Area and Surface Area of Right Prisms
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The surface area of a right rectangular prism
with length l, width w, and height h can be
written as S 2lw 2wh 2lh.
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Finding Lateral Areas and surface Areas of Prisms
Find the lateral area and surface area of each
right prism. Round to the nearest tenth, if
necessary.
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B) The regular hexagonal prism
P 6(6) 36 m
The base area is B ½aP 54 3 m.
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Now you try!
1) Find the lateral area and surface area of a
cube with edge length 8 cm.
1) lateral area 256 cm2 surface area 384 cm2
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The lateral surface of a cylinder is the curved
surface that connects the two bases. The axis of
a cylinder is the segment with endpoints at the
centers of the bases. The axis of a right
cylinder is perpendicular to its bases. The axis
of an oblique cylinder is not perpendicular to
its bases. The altitude of a right cylinder is
the same length as the axis.
Bases
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Lateral Area and Surface Area of Right Cylinders
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Finding Lateral Areas and Surface Areas of Right
Cylinders
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Step 1
Use the circumference to find the radius.
Use the radius to find the lateral area and
surface area. The height is 3 time the radius, or
15 cm.
Step 2
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Now you try!

2) lateral area 196? unit2 surface area
294? unit2
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Finding Surface Areas of composite
Three-Dimensional Figures
Find the surface area of the composite figure.
Round to the nearest tenth.
The surface area of the right rectangular prism
is S Ph 2B 80(20) 2(24)(16) 2368 ft2
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A right cylinder is removed from the rectangular
prism.
The surface area of the composite figure is the
sum of the areas of all surfaces on the exterior
of the figure.
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Now you try!
3) Find the surface area of the composite figure.
Round to the nearest tenth.
3) surface area 239.7 cm2
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Exploring Effects of Changing dimensions
The length, width, and height of the right
rectangular prism are doubled. Describe the
effect on the surface area.
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Now you try!
4) The height and diameter of the cylinder are
multiplied by ½. Describe the effect on the
surface area.
4) prev. area 1727 cm2 new area 431.75 cm2.
The surface area is decreased by 4 times.
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Chemistry Application
If two pieces of ice have the same volume, the
one with the greater surface area will melt
faster because more of it is exposed to the air.
One piece of ice shown is a rectangular prism,
and the other is half a cylinder. Given that the
volumes are approximately equal, which will melt
faster?
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Now you try!
5) Cube 2 will melt faster.
Use the information above to answer the following.
5) A piece of ice shaped like a 5 cm by 5 cm by 1
cm rectangular prism has approximately the same
volume as the pieces in the previous slide.
Compare the surface areas. Which will melt faster?
CUBE 1
CUBE 2
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Now some problems for you to practice !
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Assessment
1) How many lateral faces does a pentagonal prism
have?
1) 5 faces
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2) Find the lateral area and surface area of each
right prism.
A
B
2a) lateral area 72 ft2 surface area 142 ft2
2b) lateral area 24 cm2 surface area 36 cm2
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3a) lateral area 24? ft2 surface area 42? ft2
3b) lateral area 180? yd2 surface area
292.5? yd2
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4) Find the surface area of each composite
figure. Round to the nearest
A
B
4a) surface area 833 ft2 4b) surface area
2855.0 ft2
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5) Describe the effect of each change on the
surface area of the given figure.
A) The dimensions are cut in half.
B) The dimensions are multiplied by 2/3.
6 yd
4 yd
5a) surface area is decreased by 4 times. 5b)
surface area is decreased by 4/9 times.
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6) The greater the lateral area of a florescent
light bulb, the more light the bulb produces. One
cylindrical light bulb is 16 inches long with a
1- inch radius. Another cylindrical light bulb is
23 inches long with a ¾ inch radius. Which bulb
will produce more light?
6) second bulb will produce more light.
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Lets review
Surface Area of Prisms and Cylinders
Prisms and cylinders have 2 congruent parallel
bases. A lateral face is not a base. The edges of
the base are called base edges. A lateral edge is
not an edges of a base. The lateral faces of a
right prism are all rectangles. An oblique prism
has at least one nonrectangular lateral face.
Next Page
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An altitude of a prism or cylinder is a
perpendicular segment joining the planes of the
bases. The height of a three-dimensional figure
is the length of an altitude. Surface area is
the total area of all faces and curved surfaces
of a three-dimensional figure. The lateral area
of a prism is the sum of the areas of the lateral
faces.
Next Page
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The net of a right prism can be drawn so that the
lateral faces form a rectangle with the same
height as the prism. The base of the rectangle is
equal to the perimeter of the base of the prism.
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Lateral Area and Surface Area of Right Prisms
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The surface area of a right rectangular prism
with length l, width w, and height h can be
written as S 2lw 2wh 2lh.
36
Finding Lateral Areas and surface Areas of Prisms
Find the lateral area and surface area of each
right prism. Round to the nearest tenth, if
necessary.
Next Page
37
B) The regular hexagonal prism
P 6(6) 36 m
The base area is B ½aP 54 3 m.
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The lateral surface of a cylinder is the curved
surface that connects the two bases. The axis of
a cylinder is the segment with endpoints at the
centers of the bases. The axis of a right
cylinder is perpendicular to its bases. The axis
of an oblique cylinder is not perpendicular to
its bases. The altitude of a right cylinder is
the same length as the axis.
Bases
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Lateral Area and Surface Area of Right Cylinders
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Finding Lateral Areas and Surface Areas of Right
Cylinders
Next Page
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Step 1
Use the circumference to find the radius.
Use the radius to find the lateral area and
surface area. The height is 3 time the radius, or
15 cm.
Step 2
42
Finding Surface Areas of composite
Three-Dimensional Figures
Find the surface area of the composite figure.
Round to the nearest tenth.
Next Page
43
A right cylinder is removed from the rectangular
prism.
The surface area of the composite figure is the
sum of the areas of all surfaces on the exterior
of the figure.
44
Exploring Effects of Changing dimensions
The length, width, and height of the right
rectangular prism are doubled. Describe the
effect on the surface area.
45
Chemistry Application
If two pieces of ice have the same volume, the
one with the greater surface area will melt
faster because more of it is exposed to the air.
One piece of ice shown is a rectangular prism,
and the other is half a cylinder. Given that the
volumes are approximately equal, which will melt
faster?
Next Page
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You did a great job today!