1. 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 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 3 6-6 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 3 6-6 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 3 6-6 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 3 6-6 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 3 6-6 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 3 6-6 Volume of Prisms and Cylinders B. 4 in. 12 in. = 192 602.9 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 3 6-6 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 3 6-6 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 3 6-6 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 3 6-6 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 3 942 in 3 Insert Lesson Title Here 160.5 in 3 No; the volume would be quadrupled because you have to use the square of the radius to find the volume. Course 3 6-6 Volume of Prisms and Cylinders 10 in. 8.5 in. 3 in. 12 in. 2 in. 15 in. 10.7 in. 1.3. 2. 4. Explain whether doubling the radius of the cylinder above will double the volume.