12-106th grade math

Volume of Triangular Prisms! and Cylinders!

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.

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.

• 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

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

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

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

Try It!Find the volumes.1) Triangular prism: 7m, 4m,

5.5m2) Cylinder: r = 5 mm, h = 4

mm3) Cylinder: r = 1 ¾ ft, h = 4 ft

1) ½ x l x w x h= ½ (7 x 4) x 5.5 = 14 x 5.5= 77 m³2) 3.14 x r x r x h = 3.14 x 5 x 5 x 4 = 78.5 x 4= 314 mm³3) 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

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

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.

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.