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Unit 5 Part 1: Filling and Wrapping Guided Notes 2013Lesson 1: CirclesEssential Question –How can I find the circumference and area of circles?Vocabulary – Circle - ____________________________________________________________________________________Radius - ________________________________________________________Diameter - ________________________________________________________Circumference - ________________________________________________________Circumference of a Circle:The circumference of a circle is the ________ of ____ and the ________, or twice the product of ____ and the ______.Formulas: C = πd or C = 2πrExample 1: Finding the Circumference of a Circle217170036766500Find the circumference of the clock. Use 3.14 for π. Example 2: Finding the Circumference of a Circle251460033083500Find the circumference of the circle. Use 227 for π.Example 3: Finding the Diameter of a CircleThe largest tree in the United States is growing in Sequoia National Park in California. The tree is a giant sequoia whose trunk is roughly circular and has a circumference of 998 inches. What is the tree’s diameter?Area of a CircleThe area A of a circle is the _______ of π and the ________ of the radius.Formula: A = πr2Example 4: Finding the Area of a CircleThe central performance area at a circus is a circular ring having a diameter of 42 feet. Find the area of the ring.Your Turn:Find the circumference of the circle. Use 227 or 3.14 for π.210312012827000400685109855001.2. 3. The circumference of a circle is 22 inches long. Find the circle’s diameter. Round your answer to the nearest whole number.1792605238760004. Find the area of the circle. Use 227 or 3.14 for π. Lesson 2: AreaEssential Question –How can I find the area of different shapes?Parallelograms-The _____ of a parallelogram is the length of any one of the sides. The ______ of a parallelogram s the perpendicular distance between the side whose length is the base and the opposite side.09080500Area of a ParallelogramThe area A of a parallelogram is the ______ of a base and the __________ height.Formula: A = bh164782539814500Example 1: Finding the Area of a ParallelogramExample 2: Finding the Base of a ParallelogramA treadmill’s belt is in the shape of a parallelogram before its ends are joined to form a loop. The belt’s area is 2052 square inches. The belt’s width, which is the height of the parallelogram, is 18 inches. Find the length of the belt, which is the base of the parallelogram.Area of Triangles240030049974500The area A of a triangle is _____ the product of a base and the corresponding ______.Formula: ?bh Example 3: Finding the Area of a Triangle205740069405500To find the area of the wall of the Rock and Roll Hall of Fame and Museum described above, use the diagram shown.Example 4: Finding the Base of a TriangleA triangle has a height of 10 centimeters and an area of 35 square centimeters. Find the base of the triangle.Area of Trapezoids80010052514500The area A of a trapezoid is ____ the product of the ___ of the _______ and height.Formula: A = ?(b1 + b2)h194310036703000Example 5: Finding the area of a TrapezoidExample 6: Finding the Height of a TrapezoidA trapezoid has an area of 66 square meters. The bases are 8 meters and 14 meters. Find the height. YOUR TURN:1828800282575001. Find the unknown base or height of the parallelogram. 2. Find the area of the trapezoid.1943100178435003. You are making a reflective patch for your backpack. The patch is a triangle with a base of 12 centimeters and a height of 6 centimeters. What is the area of the patch? (HINT: Draw a picture)4. A trapezoid has an area of 180 square centimeters. The height is 5 centimeters and one base is 12 centimeters. Find the other base.Lesson 3: VolumeEssential Question –How can I find the volume of different shapes?Vocabulary – 1. Volume -_________________________________________________________.Volume of a Rectangular PrismThe volume V of a rectangular prism is the _______ of the length, width, and height.13716009461500 0128905B = area of baseh = height00B = area of baseh = heightFormula: V = lwh or V = BhVolume of a Triangular PrismThe volume of a prism is the ______ of the ____ of the base and the height.57150022225001714500136525B = area of baseh = height00B = area of baseh = heightFormula: V = Bh or V = ?(lw)h Example 1: Volume of a Rectangular PrismAn aquarium shaped like a rectangular prism has a length of 120 centimeters, a width of 60 centimeters, and a height of 100 centimeters. How much water is needed to fill the aquarium?Example 2: Finding the Volume of a Triangular Prism14859002159000Find the volume.Volume of a CylinderThe volume V of a cylinder is the product of the ______ of the base and height19431007429500Formula: V = πr2hExample 3: Finding the Volume of a Cylinder217170033083500Find the volume of the cylinder. Use 3.14 for π.Volume of a Cone114300047752000The volume of a cone is ____ _____ the product of the area of the base and the height. Formula: V = 13 Bh= 13πr2hExample 4: Finding the Volume of a Cone228600053086000Many Native American tribes built tepees that were cone-shaped. A tepee has a height of 12 feet and a base diameter of 12 feet. Approximate the volume of the tepee.Volume of a Pyramid217170040259000The volume of a pyramid is one-third the _____ of the area of the _____ and _____.Formula: V = 13BhExample 5: Finding the Volume of a Pyramid1828800116522500The Rainforest Pyramid in Galveston Island, Texas, is the home of many plants, butterflies, fish, and reptiles. This square pyramid has a height of 100 feet, and each side of its base measures 200 feet. What is the volume of the Rainforest Pyramid? 502920013398500Your Turn:Find the Volume of each figure.1943100304800045720030480001. 2. 205740012065000457200200660003. 4. Lesson 4: Surface AreaEssential Question –How can I use the concept of surface area to solve problems?36614109080500Vocabulary:1. Surface Area - ___________________________________________.2. Net - _________________________________________________.Surface Area of a Rectangular PrismThe surface area S of a rectangular prism is the _____ of the areas of its _____.80010013652500Formula: S = 2lw + 2lh + 2whExample 1: Finding the Surface Area using a Net018415000194310028067000Example 2: Finding Surface Area using a FormulaSurface Area of a Prism2533650770255B = area of baseP = perimeter base00B = area of baseP = perimeter baseThe surface area of a prism is the _____ of twice the area of a ____ and the product of the base’s ________ and height.Formula: S = 2B + Ph194310034290000Example 3: Using a Formula to find Surface AreaFind the surface are of the triangular prism.Surface Area of a Cylinder114300067183000The surface area of a cylinder is the sum of ______ the area of a base and the product of the base’s ____________ and the height.Formula: S = 2B + Ch = 2πr2 + 2πrhExample 4: Finding the Surface Area of a Cylinder194310028702000Find the surface area of the can of sloppy Joe sauce. Surface Area of a Cone240030054800500The surface of a cone is the _____ of the area of the base and the _______ of ___, the radius of the base and the _____ height.4000500-1905005715000-190500Formula: S = πr2 + πrlExample 5: Finding the Surface Area of a ConeFind the surface area of a cone with radius 4 meters and slant height 9 meters.Surface Area of a PyramidThe height of a pyramid is the perpendicular distance between the vertex and the base.91440042037000The slant height l of a regular pyramid is the height of any face that is not the base.Formula: S = B + ?PlExample 6: Finding the Surface Area of a Pyramid200977528892500Find the surface area of the regular pyramid. Your Turn:Find the surface area of each shape.18288001924050022860078105001. 2.3. 4 ................
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