Volume of Rectangular Prisms. How can you find the volume of a rectangular prism?
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1 ? Name 12.3 Essential Question Volume of Rectangular Prisms How can you find the volume of a rectangular prism? Geometry and Measurement 5.6. lso 5.4.G MTHEMTIL PROESSES 5.1.F, 5.1.G onnect The base of a rectangular prism is a rectangle. You know that area is measured in square units and that the area of a rectangle can be found by multiplying the length and the width. Volume is measured in cubic units, such as cubic feet or cu ft. When you build a prism and add each layer of cubes, you are adding a third dimension, height. The area of the base is _ sq units. Unlock the Problem Sid built the rectangular prism shown at the right, using 1-inch cubes. The prism has a base that is a rectangle and has a height of 4 cubes. What is the volume of the rectangular prism that Sid built? You can find the volume of a prism in cubic units by multiplying the number of square units in the base shape by the number of layers, or its height Each layer of Sid s rectangular prism is composed of _ inch cubes. 12 Height (in layers) Volume (in cubic inches) Multiply the height by _. 1. How does the volume change as each layer is added? Houghton Mifflin Harcourt Publishing ompany 2. What does the number you multiply the height by represent? So, the volume of Sid s rectangular prism is _ cu in. Module
2 Share and Show Find the volume. 1. The length of the rectangular prism is. The width is. So, the area of the base is. 4 cm The height is. So, the volume of the prism is. 2 cm ft Problem Solving 5 in. 4. Explain what else you need to know to find the volume of a rectangular prism if you know the area of the base. Math Talk Mathematical Processes How many more layers should be added to the prism in Exercise 3 so that the volume of the prism is 60 cubic inches? Explain. 5. Reasoning How can you find the volume of a cube if you know the area of the base is 25 sq cm? 6. The volume of a rectangular prism is 40 cu ft. The height of the prism is 10 ft. What is the area of the base of the prism? Explain. 448 Houghton Mifflin Harcourt Publishing ompany
3 Name Problem Solving 7. Kayan is designing a box for sugar cubes. Each sugar cube has a volume of 1 cubic inch. Kayan wants to have 12 cubes in each layer. If he wants to fit 60 cubes in each box, how tall should the box be? 8. Multi-Step Golf balls are packed in cardboard boxes that are 2 inches long, 2 inches wide, and 2 inches high. The boxes are then packed into larger containers that are 20 inches long, 30 inches wide, and 20 inches high. How many golf balls can fit in the larger container? 20 in. 20 in. 30 in. 9. Multi-Step Yvette uses centimeter cubes to make a bed for her doll. The bed is in the shape of a rectangular prism. She wants the length of the prism to be 1. The width should be and the height. How many centimeter cubes does Yvette need? Houghton Mifflin Harcourt Publishing ompany 10. Multi-Step ameron uses a rectangular baking pan with a base measuring 12 square inches. ameron pours batter in the pan so that it is 2 inches deep. The finished cake will be 3 times as tall as the batter. What is the volume of the cake? Module 12 Lesson 3 449
4 aily ssessment Task Mathematical Processes Fill in the bubble completely to show your answer. 11. cube-shaped block of cheese has side lengths of 6 inches. The block of cheese is cut into smaller pieces. Each piece has a volume of 1 cubic inch. How many pieces of cheese will there be? 18 pieces 36 pieces 216 pieces 72 pieces 12. Frank is packing cube-shaped containers into large boxes. He can fit 15 containers in each layer. If he stacks 8 layers into one box, what is the volume of the box? 64 cubes 128 cubes 120 cubes 256 cubes 13. Multi-Step rectangular block of cheese has a length of 8 centimeters, a width of 4 centimeters, and a height of 3 centimeters. If the block is cut into two equal pieces, what will be the volume of each piece? 15 cubic cm 28 cubic cm 48 cubic cm 96 cubic cm TEXS Test Prep 14. What is the volume of the rectangular prism at the right? 28 sq cm sq cm 28 cu cm 140 cu cm 7 cm 4 cm Houghton Mifflin Harcourt Publishing ompany
5 Homework and Practice Name Geometry and Measurement 5.6. lso 5.4.G MTHEMTIL PROESSES 5.1.F, 5.1.G 12.3 Volume of Rectangular Prisms Find the volume cm 2. 2 ft 2 cm 8 ft in. 3 cm 3 cm in. 4 ft 3 in. 5 in. 2 ft Houghton Mifflin Harcourt Publishing ompany Problem Solving 7. Vijay has a collection of 50 number cubes that are each 1 cubic inch. He finds a box that is 4 inches high. He fits 12 cubes into the bottom of the box. an Vijay fit all his number cubes into the box? Explain. 8. Maya wants to use 1-centimeter cubes to make a larger cube with side lengths of 3 centimeters. How many 1-centimeter cubes will Maya need? Module 12 Lesson 3 451
6 Lesson heck TEXS Test Prep Fill in the bubble completely to show your answer. 9. What is the volume of the rectangular prism shown below? 5 in. 10. Miranda packs cube-shaped jewelry boxes into a display box that is a rectangular prism. In the bottom layer, she can fit 4 rows of 7 jewelry boxes. If she stacks 6 layers into the display box, what is the volume of the display box? 168 cubes 12 sq in. 60 sq in. 6 in. 28 cubes 196 cubes 66 cubes 12 cu in. 60 cu in. 11. Jaden fills a box with 32 cubes. The box is 4 cubes long and 2 cubes wide. How many layers of cubes are in the box? Javier has forty 1-centimeter cubes. He builds a rectangular prism with 6 cubes in the bottom layer. He wants to have the fewest cubes left over. How many layers can Javier make? Multi-Step The shipping clerk packs a cube with side lengths of 8 inches into a box with side lengths of 10 inches. What is the volume of the space left in the larger box for packing materials? cubic inches 1,000 cubic inches 512 cubic inches 488 cubic inches 14. Multi-Step The volume of cube is 64 cubic feet. What is the volume of cube if its side lengths are half the length of cube s sides? 8 cubic feet 32 cubic feet 16 cubic feet 4 cubic feet Houghton Mifflin Harcourt Publishing ompany
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