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Surface area & volume UNIT 4

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Prisms SECTION 1

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Prism: three dimensional shape with two parallel sides Bases: sides parallel to each other Lateral faces: sides that are not the bases PRISMS

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Volume = length × width × height Example 1: Find the volume of a prism with a length of 5 inches, a width of 7 inches, and a height of 2 inches. Example 2: Find the rectangular width of a prism with a volume of 72, a length of 6, and a height of 3. RECTANGULAR PRISM

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Example 3: Find the height (in terms of x) of a rectangular prism with a volume of 4x 2 – 8x – 32, a length of 4, and a width of x – 4. Example 4: What is the longest line you can draw in this rectangular prism? CHALLENGE YOURSELF!

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Pyramids SECTION 2

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Lateral Side Base Height (Altitude) Lateral Height (“Slant height”) One base is a regular polygon (all edges congruent) Lateral faces are isosceles triangles Lateral area = area of triangles added together PYRAMID

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Pyramid Volume = Bh B = AREA of base h = height Pyramid lateral area = P l P = Perimeter of base l = Slant height Ex.: Find the volume and lateral area of a pyramid with a square base with sides of 12 inches and a height of 8 inches. PYRAMID FORMULAS 1313 1212 Base 8 l = ? 12

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Cylinders SECTION 3

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CYLINDERS Base Lateral Area

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Volume = Bh B = Area of base (B = πr 2 ) h = height r = radius Lateral Area = 2πrh Examples: Find the volume of a cylinder with a radius of 3 and a height of 10. Express your answer in terms of π. Find the lateral area of the same cylinder. Round your answer to the nearest tenth. FORMULAS FOR A CYLINDER

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Cones SECTION 4

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CONES Base Lateral Area Lateral Height (“Slant” Height) Apex

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Volume = Bh B = Area of base (B = πr 2 ) h = height, r = radius Lateral Area = πr l Where does this formula come from? Find the lateral area and surface area of a cone with a diameter of 12 and a height of 8. Express your answer in terms of π. Find the volume of the same cone to the nearest tenth. CONE FORMULAS 1313 8

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Spheres SECTION 4

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SPHERES Diameter

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Volume = πr 3 Surface Area = 4πr 2 Example: Find the volume of a sphere with a surface area of 144π. (Hint: Find the radius first!) SPHERE FORMULAS 4343

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