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Geometry

Geometry. The width, height, and length of a box or rectangular prism can be different. If all three are the same, then the box is a cube. Rectangular Prism The volume, or the amount of space inside a box, is h × w × l .

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Geometry

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  1. Geometry • The width, height, and length of a • box or rectangular prism can be • different. If all three are the same, • then the box is a cube. • Rectangular Prism • The volume, or the amount of space inside a box, is h × w × l. • The surface area of a box is 2(h × w) + 2(h × l) + 2(w × l) • A shoe box is a rectangular prism with a volume of • 6287 cm3

  2. Rectangular Prism • Find the volume of this jewelry box by using the equation for a rectangular prism: • Dimensions of the Jewelry Box: • Height = 14 cm Length = 30 cm Width = 18 cm • (ANSWER: 14 x 30 x 18 = 7,560 cm3)

  3. Geometry • The radius, r, or the distance • from the center of a sphere to • its edge, is the defining • property of a sphere. • Sphere • The diameter, or the distance across a sphere that passes through the center point, is 2r (twice the radius). • The surface area of a sphere is 4pr2. • The volume enclosed by a sphere is 4/3pr3. • Note that p=3.1415926535. • A basketball has a volume of 7700cm3 .

  4. Sphere • Find the volume of this basketball by using the equation for a sphere: • Dimensions of the Basketball: • Radius = 11.9 cm • (ANSWER: 4/3 x 3.14 x 11.9 x 11.9 x 11.9 = 7,055 cm3)

  5. GeometryThe radius, r, is thedistance from the center of a cone to its edge. • The height, h, is the • distance from the tip • of the cone to the • center of the base of • the cone. • Cone • The diameter, or the distance across the base of the cone • through the center, is 2r (twice the radius). • The surface area of a cone is p r h2 + r 2 + p r 2. • The volume of a cone is 1/3 p r 2 h. • Note that p =3.1415926535! But you can round to the • hundredths place and use 3.14. • An ice cream cone is a cone with a volume of 180cm3. _____

  6. Cone • Find the volume of this ice cream cone by using the equation for a cone: • Dimensions of the Ice Cream Cone: • Radius = 3.5 cm Height = 14 cm • (ANSWER: 1/3 x 3.14 x 3.5 x 3.5 x 14 = 179.5 cm3)

  7. Geometry If your cylinder is The radius, r, is the standing upright, you distance from the might call the “length”, center of a cylinder l, a "height" instead.to its edge. • Cylinder • The diameter, or the distance across a cylinder that passes through the center point, is 2r (twice the radius). • The surface area of an open ended cylinder (as shown) is 2pr l . • If the cylinder has caps on the ends, then the surface area is 2pr l +2pr2. • The volume of a cylinder is pr2 l . • A soda can has a volume of 335 cm3 .

  8. Cylinder • Find the volume of this spray can by using the equation for a cylinder: • Dimensions of the Spray Can: • Radius = 10 cm Length = 50 cm • (ANSWER: 3.14 x 10 x 10 x 50 = 15,700 cm3)

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