Our learning goal is to be able to solve for perimeter, area and volume. Learning Goal Assignments 1.Perimeter and Area of Rectangles and Parallelograms 2.Perimeter and Area of Triangles and Trapezoids 3.The Pythagorean Theorem 4.Circles 5.Drawing Three-Dimensional figures 6.Volume of Prisms and Cylinders 7.Volume of Pyramids and Cones 8.Surface Area of Prisms and Cylinders 9.Surface Area of Pyramids and Cones 10.Spheres

Pre-Algebra 6-6 Volume of Prisms and Cylinders Learning Goal Assignment Learn to find the volume of prisms and cylinders.

Pre-Algebra 6-6 Volume of Prisms and Cylinders Pre-Algebra HOMEWORK Page #

Pre-Algebra 6-6 Volume of Prisms and Cylinders 6-6 Volume of Prisms and Cylinders Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Pre-Algebra 6-6 Volume of Prisms and Cylinders Warm Up Make a sketch of a closed book using two-point perspective. Pre-Algebra 6-6 Volume of Prisms and Cylinders

Pre-Algebra 6-6 Volume of Prisms and Cylinders Math Warm Up Make a sketch of a closed book using two-point perspective. Possible answer:

Pre-Algebra 6-6 Volume of Prisms and Cylinders Problem of the Day You are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another? only 2

Pre-Algebra 6-6 Volume of Prisms and Cylinders Learning Goal Assignment Learn to find the volume of prisms and cylinders.

Pre-Algebra 6-6 Volume of Prisms and Cylinders Vocabulary prism cylinder

Pre-Algebra 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.

Pre-Algebra 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

Pre-Algebra 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

Pre-Algebra 6-6 Volume of Prisms and Cylinders Area is measured in square units. Volume is measured in cubic units. Helpful Hint

Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Additional Example 1A: Finding the Volume of Prisms and Cylinders A. A rectangular prism with base 2 cm by 5 cm and height 3 cm. = 30 cm 3 B = 2 5 = 10 cm 2 V = Bh = 10 3 Area of base Volume of a prism

Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. A. A rectangular prism with base 5 mm by 9 mm and height 6 mm. = 270 mm 3 B = 5 9 = 45 mm 2 V = Bh = 45 6 Area of base Volume of prism Try This: Example 1A

Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. 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

Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. 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

Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. C. 5 ft 7 ft 6 ft V = Bh = 15 7 = 105 ft 3 B = 6 5 = 15 ft Additional Example 1C: Finding the Volume of Prisms and Cylinders Area of base Volume of a prism

Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. C. 10 ft 14 ft 12 ft = 60 ft 2 = 60(14) = 840 ft 3 Try This: Example 1C Area of base Volume of a prism B = V = Bh

Pre-Algebra 6-6 Volume of Prisms and Cylinders A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds. Additional Example 2A: Exploring the Effects of Changing Dimensions The original box has a volume of 24 in 3. You could triple the volume to 72 in 3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

Pre-Algebra 6-6 Volume of Prisms and Cylinders A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. Try This: Example 2A Tripling the length would triple the volume. V = (15)(3)(7) = 315 cm 3 The original box has a volume of (5)(3)(7) = 105 cm 3.

Pre-Algebra 6-6 Volume of Prisms and Cylinders A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. Try This: Example 2A The original box has a volume of (5)(3)(7) = 105 cm 3. Tripling the height would triple the volume. V = (5)(3)(21) = 315 cm 3

Pre-Algebra 6-6 Volume of Prisms and Cylinders A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. Try This: Example 2A Tripling the width would triple the volume. V = (5)(9)(7) = 315 cm 3 The original box has a volume of (5)(3)(7) = 105 cm 3.

Pre-Algebra 6-6 Volume of Prisms and Cylinders 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 By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

Pre-Algebra 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.

Pre-Algebra 6-6 Volume of Prisms and Cylinders 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 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.

Pre-Algebra 6-6 Volume of Prisms and Cylinders A section of an airport runway is a rectangular prism measuring 2 feet thick, 100 feet wide, and 1.5 miles long. What is the volume of material that was needed to build the runway? Additional Example 3: Construction Application length = 1.5 mi = 1.5(5280) ft = 7920 ft height = 2 ft = 1,584,000 ft 3 The volume of material needed to build the runway was 1,584,000 ft 3. width = 100 ft V = ft 3

Pre-Algebra 6-6 Volume of Prisms and Cylinders A cement truck has a capacity of 9 yards 3 of concrete mix. How many truck loads of concrete to the nearest tenth would it take to pour a concrete slab 1 ft thick by 200 ft long by 100 ft wide? Try This: Example 3 V = 20,000(1) B = 200(100) = 20,000 ft 2 = 20,000 ft 3 27 ft 3 = 1 yd 3 20,  yd = 82.3 Truck loads

Pre-Algebra 6-6 Volume of Prisms and Cylinders Additional Example 4: Finding the Volume of Composite Figures Find the volume of the the barn. Volume of barn Volume of rectangular prism Volume of triangular prism + = = 30, ,000 V = (40)(50)(15) + (40)(10)(50) 1212 = 40,000 ft 3 The volume is 40,000 ft 3.

Pre-Algebra 6-6 Volume of Prisms and Cylinders Try This: Example 4 Find the volume of the figure. 3 ft 4 ft 8 ft 5 ft = (8)(3)(4) + (5)(8)(3) 1212 = V = 156 ft 3 Volume of barn Volume of rectangular prism Volume of triangular prism + =

Pre-Algebra 6-6 Volume of Prisms and Cylinders Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for . 306 in in in 3 No; the volume would be quadrupled because you have to use the square of the radius to find the volume. 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.