Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up 1. A triangular pyramid has a base area
of 1.2 m2 and a height of 7.5 m. What is the
volume of the pyramid? 2. A cone has a radius
of 4 cm and a height of 10 cm. What is the volume
of the cone to the nearest cubic centimeter? Use
3.14 for p.
3 m3
167 cm3
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Vocabulary
surface area lateral face lateral area lateral
surface
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The surface area of a three-dimensional figure is
the sum of the areas of all its surfaces. You can
use centimeter cubes to explore the surface area
of prisms.
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Additional Example 1A Finding Surface Area of
Figures Built of Cubes
Find the surface area of each figure. The figure
is made up of congruent cubes.
Draw each view of the figure.
top
front
left
1 cm
1 cm
Find the area of each view.
bottom
back
right
12 8 6 12 8 6 52
The surface area is 52 cm2.
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Additional Example 1B Finding Surface Area of
Figures Built of Cubes
Find the surface area of each figure. The figure
is made up of congruent cubes.
Draw each view of the figure.
top
front
left
1 cm
1 cm
Find the area of each view.
bottom
back
right
8 8 6 8 8 6 44
The surface area is 44 cm2.
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Check It Out! Example 1A
Find the surface area of each figure. The figure
is made up of congruent cubes.
Draw each view of the figure.
top
front
left
1 cm
1 cm
Find the area of each view.
bottom
back
right
8 8 4 8 8 4 40
The surface area is 40 cm2.
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Check It Out! Example 1B
Find the surface area of each figure. The figure
is made up of congruent cubes.
Draw each view of the figure.
top
front
left
1 cm
1 cm
Find the area of each view.
bottom
back
right
8 9 6 8 9 6 46
The surface area is 46 cm2.
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The lateral faces of a prism are parallelograms
that connect the bases. The lateral area of a
prism is the sum of the areas of the lateral
faces.
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Additional Example 2 Finding Surface Area of
Prisms
Find the surface area of the figure to the
nearest tenth.
The figure is a triangular prism.
S 2B Ph
204 ft2
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Check It Out! Example 2
Find the surface area of the figure to the
nearest tenth.
The figure is a triangular prism.
S 2B Ph
7 cm
7 cm
6 cm
252 cm2
10 cm
7 cm
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The lateral surface of a cylinder is the curved
surface.
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Additional Example 3 Finding Surface Area of
Cylinders
Find the surface area of the cylinder to the
nearest tenth. Use 3.14 for p.
S 2pr2 2prh
2p(42) 2p(4)(6)
80p in2 ? 251.2 in2
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Check It Out! Example 3
Find the surface area of the cylinder to the
nearest tenth. Use 3.14 for p.
15 cm
S 2pr2 2prh
3 cm
2p(152) 2p(15)(3)
540p in2 ? 1695.6 cm2
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Additional Example 4 Application
A cylindrical soup can is 7.6 cm in diameter and
11.2 cm tall. Estimate the area of the label that
covers the side of the can.
The cylinders diameter is about 8 cm, and its
height is about 11 cm.
Only the lateral surface needs to be covered.
L 2?rh
2?(4)(11)
Diameter 8 cm, so r 4 cm.
88? 267.3 cm2
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Check It Out! Example 4
A cylindrical storage tank that is 6 ft in
diameter and 12 ft tall needs to be painted.
Estimate the area to be painted.
S 2?r2 2?rh
The diameter is 6 ft, so r 3 ft.
2?(32) 2?(3)(12)
90? ft2 ? 282.6 ft2
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Lesson Quiz
Find the surface area of each figure to the
nearest tenth. Use 3.14 for p. 1. the triangular
prism 2. the cylinder
360 cm2
320.3 in2
3. All outer surfaces of a box are covered with
gold foil, except the bottom. The box measures 6
in. long, 4 in. wide, and 3 in. high. How much
gold foil was used?
84 in2