chapter 10: area & volume 10.4, 10.5, 10.6 space figures surface area of prisms, cylinders,...
TRANSCRIPT
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Chapter 10: Area & Volume
10.4, 10.5, 10.6Space Figures
Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres
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Space Figures• common three-dimensional figures
• prisms: two parallel bases that are congruent polygons, lateral faces that are parallelograms
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Space Figures
• Pyramids:base that is a polygon, lateral faces are triangles
• Cylinders:two parallel bases that are congruent circles
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Space Figures
• Cones: one circular base and one vertex
• Sphere: set of all points in space that are a given distance from a given point called the center
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Example 1• For each figure, describe the bases and name
the figure.
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Example 2
• Name the space figure you can form from each net:
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Example 2a• Name the space figure you can form from each
net:
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Surface Area
• abbreviated S.A.
• sum of the areas of the base(s) and the lateral faces of a space figure
• one way to find it: find the area of each piece of the space figure’s net
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Example 1
• Find the surface area of the rectangular prism using a net.
8 in
5 in20 in
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Example 1a
• Find the surface area of the triangular prism:6 yd
5 yd
4 yd
3 yd
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Example 2
• Find the surface area of the triangular prism at the right.
12 cm
5 cm
6 cm
4 cm5 cm
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Surface Area of a Prism
• lateral area: LA = ph– perimeter of base times height
• surface area: SA = LA + 2B– lateral area plus the area of the two bases
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Surface Area of a Cylinder
• lateral area: LA = 2πrh– twice pi times the radius of the base times the
height
• surface area: SA = LA + 2B
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Example 3
• Find the surface area of the can:
11.5 cm
7 cm
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Example 3a
• Find the surface area of a can with radius 5 cm and height 20 cm.
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Surface Area of a Pyramid
• lateral area: LA = ½ pl– ½ perimeter of the base times the slant height
• surface area: SA = LA + B– lateral area plus the area of the base
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Example 1
• Find the surface area of the square pyramid:
16 cm
12 cm12 cm
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Surface Area of a Cone
• lateral area: LA = πrl– pi times radius times slant height
• surface area: SA = LA + B– lateral area plus area of the base
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Example 2
• Find the surface area of the cone:
4 cm
10 cm
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Surface Area of a Sphere
24 rSA
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Example 3
• Calculate the surface area of a basketball:
10 in
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Homework
• p. 541: 2-12 even, 21-23
• p. 548: 4-12 all
• p. 555: 1-12 all