Name 13-6A. 1. Which is the volume of the solid? 2. What is the volume of the solid? A 72 cm 3 B 432 cm 3 C 672 cm 3 D 864 cm 3
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1 . Which is the volume of the solid? Quick Check. What is the volume of the solid? 8 in. 9 in. 8 in. A 96 in B 9 in C 0 in D 6 in 8 in. A 7 B C 67 D 86. Writing to Explain Carlos is an architect. He wants to build a skyscraper and creates this model to help him plan. Carlos believes that the upper part of the building has a greater volume than the lower part of the building. Explain whether or not he is correct. How can this help you find the volume of the entire model? What is this volume? in. Q 6A
2 Partner Talk Share your thinking while you work. Get Started or Repeat for Each Round Get paper and a pencil. Put in a bag. Choose a, b, c, or d. Pick two tiles if your group has only two students. To find your job, find the number that matches the tile you chose. Do the jobs listed below in order. Work with your team to determine how the solid figure can be divided into two more familiar shapes. Find the volume of one of the familiar shapes. Find the volume of the second familiar shape. Find the total volume of the solid figure. a b 5 ft ft c 9 m m 7 m 7 m d If you have more time Choose a or c. Find more than one way to divide the solid figure into two familiar shapes. Calculate the volume of the figure both ways. Center Activity H
3 Partner Talk Share your thinking while you work. Get Started or Repeat for Each Round Get paper and a pencil. Put in a bag. Choose a, b, c, or d. Pick a tile. Pick two tiles if your group has only two students. Do the jobs listed below in order. To find your job, find the number that matches the tile you chose. Work with your team to determine where lines can be drawn to divide the given figure into two or more familiar parts. Work with your team to find the volume of one of the familiar parts. Work with your team to find the volume of the remaining part or parts. Work with your team to find the total volume of the original irregular solid. a 7 in. b m 7 in. 0 in. c d 8 ft ft ft If you have more time Choose a, b, c or d. Discuss whether or not the irregular solid could have been divided into familiar parts in a different way. Center Activity HH
4 Combining Volumes Reteaching To find the volume of a solid made up of familiar parts, find the volume of each part and add the volumes. Step : To find the volume of the figure at the right, separate the solid into two rectangular prisms. (See the dotted line in the figure.) 5 ft ft Prism A Prism B ft Step : Use the formula Volume of Prism A Volume of Prism B V = w h to find the volume of each prism. V = 7 = 8 ft V = = 6 ft Step : Add the volumes The volume of the solid is = ft. of each prism.. Show two ways of dividing the given solid into two rectangular solids.. Find the volume of the rectangular solid shown below. Show your work. cm R 6A
5 Combining Volumes For through, find the volume of each solid figure. Practice. 9 in. 9 in.. ft ft 5 ft. 0 cm. 7 in. 0 cm 0 cm 5. Paul wants to build this model with clay, but he does not know how many cubic centimeters of clay to purchase. How much clay should he purchase? A C 0 B D 9 6. Ashley is stacking two boxes on a shelf. The bottom box measures 6 inches 5 inches 5 inches. The top box is a cube with one edge measuring inches. What is the volume of this stack? Explain how you found your answer. 9 cm P 6A
6 Volume of Solids. Jim has a box in the shape of a rectangular prism. The area of the base of the box is 8 square inches. The volume of the box is cubic inches. Let h = the height of Jim s box. Write and solve an equation you can use to find the height of Jim s box. Enrichment. The volume of a rectangular prism is 70 cubic centimeters. The height of the prism is 5 centimeters. What could the length and width of the prism be? Explain your solution strategy.. A prism has a volume of 5 cubic feet. The width of the prism is 8 feet. Could this prism be a cube? Why or why not? For and 5, draw two solids that have a combined volume of 7 in. Label the dimensions of each drawing.. Rectangular Prism A 5. Cube A Rectangular Prism B Rectangular Prism B Combined volume Combined volume E 6A
7 Combining Volumes Teaching Tool 7 TT 7
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