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Volume of a Cone, Cylinder & Sphere r

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Volume of a Cone

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Formula: V=1/3Bh or ⅓π r²∙h 3 ft. 7 ft. ⅓ ( 3.14 ) 3²· 7 ⅓ ( 3.14 ) 9 ∙ 7 ⅓π r²∙h ⅓ ( 197.82 ) 65.94 ft³ In this case, the base is a circle. The area formula for a circle is r 2

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Examples: V=1/3Bh 9m 6m ⅓π r²∙h ⅓ ( 3.14 ) 6²· 9 ⅓ ( 3.14 ) 36 ∙ 9 ⅓ ( 1017.36 ) 339.12 m³

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Examples: V=1/3Bh ⅓π r²∙h 13m 18m ⅓ ( 3.14 ) 9²· 13 ⅓ ( 3.14 ) 81 ∙ 13 ⅓ ( 3306.42 ) 1102.14 m³

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Using Formulas To find the volume a cylinder, multiply the area of the base by the height. Volume = Area of Base x height V = Bh (The capital B does not stand for base, it stands for area of the base.)

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Volume of a Cylinder 5 in 16 in V = Bh In this case, the base is a circle. The area formula for a circle is r 2 V = ( r 2 ) x h V = (3.14)(5 2 )(16) V = (3.14)(25)(16) V = 1,256 in 3

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24 in 8 in V = Bh V = ( r 2 ) x h V = (3.14)(8 2 )(24) V = (3.14)(64)(24) V = 4823.04 in 3 Example 2:

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6 in 14 in V = Bh V = ( r 2 ) x h V = (3.14)(6 2 )(14) V = (3.14)(36)(14) V = 1582.56 in 3 Example 3:

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Volume of Spheres r

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Spheres Sphere is the mathematical word for “ball.” It is the set of all points in space a fixed distance from a given point called the center of the sphere. A sphere has a radius and diameter, just like a circle does. The volume of a sphere is: r

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Spheres Sphere – The set of all points in space equidistant from a given point. Center r Radius – Is a segment that has one endpt @ the center & the other endpt on the sphere. Diameter – A segment passing through the center w/ both endpts on the sphere.

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Volume of a sphere V s = (4/3) r 3 Radius of a sphere r

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Ex.: Find the volume of the following sphere. 30m V s = (4/3) r 3 = (4/3) (15) 3 = (4/3) (3375) = 4500 = 14130m 3

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Ex.: Find the volume of the following sphere. 9 in. V s = (4/3) r 3 = (4/3) (9) 3 = (4/3) (729) = 972 = 3052.08in 3

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What have we learned?? V s = (4/3) r 3 Radius of a sphere r

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1-5: USING FORMULAS IN GEOMETRY. PERIMETER & AREA RectangleSquareTriangle P = 2l + 2w or 2(l + w) A = lw P = 4s A = s 2 P = a + b + c A = ½ bh.

1-5: USING FORMULAS IN GEOMETRY. PERIMETER & AREA RectangleSquareTriangle P = 2l + 2w or 2(l + w) A = lw P = 4s A = s 2 P = a + b + c A = ½ bh.

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