Volume of Prisms Focus 12 Learning Goal The

Volume of Prisms

Focus 12 - Learning Goal: The student will know and use the formulas for volume of cones, cylinders and spheres. 4 3 2 In addition The student With no help to 3, student will know and the student will be able use the has a partial to go above formulas for understandin and beyond volume of g of volume by applying cones, of cones, what they cylinders and know about spheres. volume of - Students cones, can apply spheres and these cylinders. formulas to solve real world mathematical problems. 1 0 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.

Definitions A prism is a threedimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms.

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

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

How to Find 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

Find the volume of the rectangular prism 8. 5 in . 6 in. Step 1: Determine what shape the base is: Rectangle Step 2: Find the area of the base (8. 5)(5) = 42. 5 Step 3: Multiply by the height: 42. 5(6) = 255 in 3

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

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

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 = (14 • 3)h The height is 9 m. • 378 = 42 h • 9 = h

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.