1. Volume of Prisms

2. 43210 In addition to 3, student will be able to go above and beyond by applying what they know about volume of cones, spheres and cylinders. The student will know and use the formulas for volume of cones, cylinders and spheres. - Students can apply these formulas to solve real- world mathematica l problems. With no help the student has a partial understandin g of volume of cones, cylinders and spheres. With help, the student may have a partial understandin g of volume of cones, cylinders and spheres. Even with help, the student is unable to find the volume of cones, cylinders and spheres. Focus 12 - Learning Goal: The student will know and use the formulas for volume of cones, cylinders and spheres.

3. Definitions 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.

4. Every prism is named by its BASE. Height Triangular prism Base

5. If all six faces of a rectangular prism are squares, it is a cube. Remember!

6. Volume of all prisms and cylinders is found by multiplying the area of the base times the height. Step 1: Decide what shape the base is. (rectangle, triangle or circle) Step 2: Find the area of the base. Step 3: Multiply by height. Formula: V = Bh V = Volume, B = area of the base, h = height of prism How to Find Volume

7. Find the volume of the rectangular prism Step 1: Determine what shape the base is: Rectangle Step 2: Find the area of the base (8.5)(5) = Step 3: Multiply by the height: 42.5(6) = 8.5 in. 5 in. 6 in. 42.5 255 in 3

8. Find the volume of the triangular prism 10 ft 12 ft 14 ft Step 1: Determine what shape the base is: Triangle Step 2: Find the area of the base ½ (12)(10) = Step 3: Multiply by the height: 60(14)= 840 ft 3 60 To find the area of a triangle multiply ½(base)(height) 10 ft 12 ft

9. Steps for finding Volume: 1.Find the area of the base. 2.Multiply by height. 3.All units used are cubed ( 3 )

10. Working the problem backwards: The volume of a rectangular prism is 378 m 3. The length of the rectangular base is 14 m the width of the rectangular base is 3 m. What is the height of the prism? To find the volume of a prism, you find the area of the base then multiply by the height. Since we are missing the height, work the problem backward. V = Bh 378 = (143)h 378 = 42h 9 = h The height is 9 m.

11. Working the problem backwards: The volume of a triangular prism is 54 in 3. The area of the triangular base is 6 in 2. What is the height of the prism? To find the volume of a prism, you find the area of the base then multiply by the height. Since we are missing the height, work the problem backward. V = Bh 54 = (6)h 9 = h The height is 9 in.