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9-2 Volume of Prisms and CylindersLearn to find the volume of prisms andcylinders.Course 2

9-2 VolumeInsert LessonTitleHereof PrismsandCylindersVocabularyvolumeCourse 2

9-2 Volume of Prisms and CylindersAny solid figure can be filled completely withcongruent cubes and parts of cubes. The volumeof a solid is the number of cubes it can hold. Eachcube represents a unit of measure called a cubicunit.Course 2

9-2 Volume of Prisms and CylindersAdditional Example 1: Using Cubes to Find theVolume of a Rectangular PrismFind how many cubes the prism holds. Thengive the prism’s volume.You can find the volume ofthis prism by counting howmany cubes tall, long, andwide the prism is and thenmultiplying.1 · 4 · 3 12There are 12 cubes in the prism, so the volume is 12cubic units.Course 2

9-2 InsertTitleandHereVolumeLessonof PrismsCylindersTry This: Example 1Find how many cubes the prism holds. Thengive the prism’s volume.You can find the volume ofthis prism by counting howmany cubes tall, long, andwide the prism is and thenmultiplying.2 · 4 · 3 24There are 24 cubes in the prism, so the volume is 24cubic units.Course 2

9-2 Volume of Prisms and CylindersA cube that measures onecentimeter on each siderepresents one cubic centimeterof volume. Suppose the cubes inthe prism in Additional Example 1measure one centimeter on eachside. The volume of the prismwould be 12 cm3.Volume 1 cm31 cm1 cm1 cmThis volume is found by multiplying the prism’s lengthtimes its width times its height.Reading MathAny unit of measurement with an exponent of 3 is a cubicunit. For example, cm3 means “cubic centimeter” and in3means “cubic inch.”Course 2

9-2 Volume of Prisms and Cylinders34cm·3cm·1cm 12cm1 cmlength · width · height volume3 cm4 cmarea ofbase· height volumeNotice that for the rectangular prism, thevolume is found by multiplying the area of itsbase times its height. This method can beused for finding the volume of any prism.VOLUME OF A PRISMThe volume V of a prism is the area of its base Btimes its height h.V BhCourse 2

9-2 Volume of Prisms and CylindersAdditional Example 2: Using a Formula to Find theVolume of a PrismFind the volume of the prism to the nearesttenth.4.1 ft4.1 ft12 ftV BhUse the formula.The bases are rectangles.The area of each rectangular base is 12 · 4.1 49.2V 49.2 · 4.1 Substitute for B and h.Multiply.V 201.72The volume to the nearest tenth is 201.7 ft3.Course 2

9-2 Volume of Prisms and CylindersTry This: Example 2Find the volume of the prism to the nearesttenth.6.3 ft6.3 ft8 ftV BhUse the formula.The bases are rectangles.The area of each rectangular base is 8 · 6.3 50.4V 50.4 · 6.3 Substitute for B and h.Multiply.V 317.52The volume to the nearest tenth is 317.5 ft3.Course 2

9-2 Volume of Prisms and CylindersFinding the volume of a cylinder is similar to findingthe volume of a prism.VOLUME OF A CYLINDERThe volume V of a cylinder is the area of its base, r2, times its height h.V r2hCourse 2

9-2 Volume of Prisms and CylindersAdditional Example 3: Using a Formula to Find theVolume of a CylinderFind the volume of a cylinder to the nearesttenth. Use 3.14 for .V r2hUse the formula.The radius of the cylinder is 5 m, andthe height is 4.2 mV 3.14 · 52 · 4.2 Substitute for r and h.V 329.7Multiply.The volume is about 329.7 m3.Course 2

9-2 InsertTitleandHereVolumeLessonof PrismsCylindersTry This: Example 3Find the volume of a cylinder to the nearesttenth. Use 3.14 for .V r2h7m3.8 mUse the formula.The radius of the cylinder is 7 m, andthe height is 3.8 mV 3.14 · 72 · 3.8 Substitute for r and h.V 584.668Multiply.The volume is about 584.7 m3.Course 2

9-2 VolumeInsert Lessonof PrismsTitleandHereCylindersLesson QuizFind the volume of each solid to the nearesttenth. Use 3.14 for .1.4,069.4 m32.861.8 cm33. triangular prism: base area 24 ft2, height 13 ft312 ft3Course 2

Homework9-2 Worksheet

9-2 Volume of Prisms and Cylinders Find how many cubes the prism holds. Then give the prism’s volume. You can find the volume of this prism by counting how many cubes tall, long, and wide the prism is and then multiplying. 2 · 4 · 3 24 There are 24 cubes in the prism, so the volume is 24 cubic units.

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