Learn to find the volume of cylinders .

1. 6-6 Volume of Prisms and Cylinders Course 3 Essential Question: Describe what happens to the volume of a cylinder when the diameter of the base is tripled. Learn to find the volume of cylinders. Objective: 8.G.9 (note that volume of prisms are no longer an 8th grade objective; however, students need to be familiar with what a prism is and how to name it.)

2. 6-6 Volume of Prisms and Cylinders Course 3 Insert Lesson Title Here Vocabulary prism cylinder Don’t forget these formula’s! You will need them! A=bh A=1/2bh A=1/2h(b1+b2) A=∏r2

3. 6-6 Volume of Prisms and Cylinders Course 3 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. 6-6 Volume of Prisms and Cylinders Remember! If all six faces of a rectangular prism are squares, it is a cube. Course 3 Rectangular prism Cylinder Triangular prism Height Height Height Base Base Base

5. 6-6 Volume of Prisms and Cylinders Course 3 VOLUME OF PRISMS AND CYLINDERS B = 2(5) = 10 units2 V = Bh V = 10(3) = 30 units3 Note that you have to find the Area of the bases first… B = p(22) V = Bh = 4p units2 = (pr2)h V = (4p)(6) = 24p 75.4 units3

6. 6-6 Volume of Prisms and Cylinders Helpful Hint Area is measured in square units. Volume is measured in cubic units. Course 3 Must label your answers appropriately! i.e. 30 cm3 or 219 units2 These are the labels…

7. 6-6 Volume of Prisms and Cylinders Course 3 Additional Example 1B: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. B. B = p(42) = 16pin2 Area of base 4 in. Volume of a cylinder V = Bh 12 in. = 16p• 12 = 192p  602.9 in3

8. 6-6 Volume of Prisms and Cylinders Course 3 Try This: Example 1B Find the volume of the figure to the nearest tenth. B = p(82) Area of base B. 8 cm = 64p cm2 Volume of a cylinder V = Bh 15 cm = (64p)(15) = 960p 3,014.4 cm3

9. 6-6 Volume of Prisms and Cylinders Course 3 Additional Example 2B: Exploring the Effects of Changing Dimensions 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. By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

10. 6-6 Volume of Prisms and Cylinders Course 3 Try This: Example 2B 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. The original cylinder has a volume of 4 • 3 = 12 cm3. V = 36 • 3= 108cm3 By tripling the radius, you would increase the volume nine times.

11. 6-6 Volume of Prisms and Cylinders Course 3 Try This: Example 2B 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. The original cylinder has a volume of 4 • 3 = 12 cm3. V = 4 • 9= 36cm3 Tripling the height would triple the volume.

12. 6-6 Volume of Prisms and Cylinders Course 3 Insert Lesson Title Here Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for p. 10 in. 1. 3. 2 in. 2. 12 in. 12 in. 10.7 in. 15 in. 3 in. 8.5 in. 942 in3 160.5 in3 306 in3 4. Explain whether doubling the radius of the cylinder above will double the volume. No; the volume would be quadrupled because you have to use the square of the radius to find the volume.