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Learn to find the volume of cylinders. Course 3 6-6 Volume of Prisms and Cylinders Essential Question: Describe what happens to the volume of a cylinder.

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Presentation on theme: "Learn to find the volume of cylinders. Course 3 6-6 Volume of Prisms and Cylinders Essential Question: Describe what happens to the volume of a cylinder."— Presentation transcript:

1 Learn to find the volume of cylinders. Course Volume of Prisms and Cylinders Essential Question: Describe what happens to the volume of a cylinder when the diameter of the base is tripled. Objective: 8.G.9 (note that volume of prisms are no longer an 8 th grade objective; however, students need to be familiar with what a prism is and how to name it.)

2 Vocabulary prism cylinder Insert Lesson Title Here Course Volume of Prisms and Cylinders Don’t forget these formula’s! You will need them! A=bh A=1/2bh A=1/2h(b 1 +b 2 ) A=∏r 2

3 Course Volume of Prisms and Cylinders A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms. A cylinder has two circular bases. All solids we know have 2 congruent bases.

4 Course Volume of Prisms and Cylinders If all six faces of a rectangular prism are squares, it is a cube. Remember! Height Triangular prism Rectangular prism Cylinder Base Height Base Height Base

5 Course Volume of Prisms and Cylinders VOLUME OF PRISMS AND CYLINDERS WordsNumbersFormula Prism: The volume V of a prism is the area of the base B times the height h. Cylinder: The volume of a cylinder is the area of the base B times the height h. B = 2(5) = 10 units 2 V = 10(3) = 30 units 3 B = (2 2 ) = 4 units 2 V = (4)(6) = 24  75.4 units 3 V = Bh = (r 2 )h Note that you have to find the Area of the bases first…

6 Course Volume of Prisms and Cylinders Area is measured in square units. Volume is measured in cubic units. Helpful Hint Must label your answers appropriately! i.e. 30 cm 3 or 219 units 2 These are the labels…

7 Find the volume of the figure to the nearest tenth. Course Volume of Prisms and Cylinders B. 4 in. 12 in. = 192 in 3 B = (4 2 ) = 16 in 2 V = Bh = 16 12 Additional Example 1B: Finding the Volume of Prisms and Cylinders Area of base Volume of a cylinder

8 Find the volume of the figure to the nearest tenth. Course Volume of Prisms and Cylinders B. 8 cm 15 cm B = (8 2 ) = 64 cm 2 = (64)(15) = 960  3,014.4 cm 3 Try This: Example 1B Area of base Volume of a cylinder V = Bh

9 A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius. Additional Example 2B: Exploring the Effects of Changing Dimensions Course Volume of Prisms and Cylinders By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

10 Course Volume of Prisms and Cylinders By tripling the radius, you would increase the volume nine times. A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. Try This: Example 2B V = 36 3 = 108 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

11 A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. Try This: Example 2B Course Volume of Prisms and Cylinders Tripling the height would triple the volume. V = 4 9 = 36 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

12 Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for . 306 in in 3 Insert Lesson Title Here in 3 No; the volume would be quadrupled because you have to use the square of the radius to find the volume. Course Volume of Prisms and Cylinders 10 in. 8.5 in. 3 in. 12 in. 2 in. 15 in in Explain whether doubling the radius of the cylinder above will double the volume.


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