12-10 6 th grade math

1. 12-106th grade math Volume of Triangular Prisms! and Cylinders!

2. Objective • To find volume of triangular prisms and cylinders • Why? To know how to use formulas and evaluate variable expressions using the order of operations. To further your knowledge of geometry and measurement.

3. California State Standards MG 1.3: Know and use … the formula for the volume of a rectangular solid. MG 1.2: Know common estimates of Π (pi) (3.14, 22/7) and use these values to estimate and calculated the circumference … of circles; compare with actual measurements AF 3.1: Use variables in expressions describing geometric quantities AF 3.2: Express in symbolic form simple relationships arising from geometry. MR 1.3: Determine when and how to break a problem into simpler parts. MR 2.2: Apply strategies and results from simpler problems to more complex problems.

4. Use what you know about the area of triangles or circles to find the volume of triangular prisms or cylinders. • All a prism or a cylinder is is a number of stacked prisms or cylinders to ‘build’ it up. This is the height. • The basis of the formula for all volumes is the base x height. • Rectangular or square prism: B (l x w) x h • Triangular prism: B ( ½ x (l x w)) x h • Cylinder: B (3.14 x r²) x h

5. Vocabulary • Cylinder • A solid whose base is a circle • V= B‧h (B = 3.14 x r²) • Triangular prism • A prism whose base, or sides, is a triangle • V = B‧h (B = ½ ‧l ‧ w) • Volume of a solid (A prism) • The number of unit cubes it will fit into a space figure • Filling the solid

6. How to Find the Volume of Triangular Prisms 1) Observe or draw the figure. Be sure all measurements are in equal labels. Write the formula: ½ (B x h) or ½ (l x w) x h 2) ½ one of the sides. Or multiply (l and w and h) 1/2. 3) Check work and add label³ to answer. Triangular prism dimensions: 8 ft, 3 ft, 6 ½ ft = (8 x 3 x 6.5) ‧ ½ = (156) ‧ ½ = 78 ft³

7. How to Find the Volume of Cylinders 1) Observe or draw the figure. Be sure all measurements are in equal labels. Write the formula: B x h or (3.14 x r x r) x h 2) Multiply the B: 3.14 x r x r and h 3) Check work and add label³ to answer. r = 2 cm 8.5 cm 3.14 x 2 x 2 x 8.5 = 107.76 cm³

8. Try It! Find the volumes. • Triangular prism: 7m, 4m, 5.5m • Cylinder: r = 5 mm, h = 4 mm • Cylinder: r = 1 ¾ ft, h = 4 ft • ½ x l x w x h = ½ (7 x 4) x 5.5 = 14 x 5.5 = 77 m³ 2) 3.14 x r x r x h = 3.14 x 5 x 5 x 4 = 78.5 x 4 = 314 mm³ 3) 3.14 x r x r x h = 3.14 x 1.75 x 1.75 x 4 = 9.61625 x 4 = 38.465 ft³ or 38.5 ft³

9. Try One More! 5) Volume of crystal vase. Dimensions: 5.6 in, 5 in, 11 in 5) ½ x l x w x h = ½ 5.6 x 5 x 11 = 2.8 x 55 = 154 in³

10. Objective Review • To find volume of triangular prisms and cylinders • Why? You now know how to use formulas and evaluate variable expressions using the order of operations. You have furthered your knowledge of geometry and measurement. • The formula for finding the volume of any prism or cylinder is V = Bh. Find the area of the base (area of a triangle or circle), then multiply by the height.

11. Independent Practice • Complete problems 6-12 • Copy original problem first. • Show all work! • If time, complete Mixed Review: 14-25 • If still more time, work on Accelerated Math.