Volumes of Rectangular Prisms
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- Scarlett Osborne
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1 . Volues of Rectangular Priss How can you find the volue of a rectangular pris with fractional edge lengths? Recall that the volue of a three-diensional figure is a easure of the aount of space that it occupies. Volue is easured in cubic units. A unit cube is a cube with an edge length of unit. unit unit unit ACTIVITY: Using a Unit Cube Work with a partner. The parallel edges of the unit cube have been divided into,, and equal parts to create saller rectangular priss that are identical. equal parts Geoetry In this lesson, you will find the volue of priss with fractional edge lengths by using odels. find the volue of priss by using forulas. equal parts equal parts a. Draw one of these identical priss and label its diensions. b. What fraction of the volue of the unit cube does one of these identical priss represent? Use this value to find the volue of one of the identical priss. Explain your reasoning. Chapter Surface Area and Volue
2 ACTIVITY: Finding the Volue of a Rectangular Pris Work with a partner. Math Practice Analyze Relationships What is the relationship between the solid shown here and the solid in the previous activity? a. How any of the identical priss in Activity (a) does it take to fill the rectangular pris below? Support your answer with a drawing. units unit unit b. Use the volue of one of the identical priss in Activity (a) to find the volue of the rectangular pris above. Explain your reasoning. ACTIVITY: Finding the Volues of Rectangular Priss Work with a partner. Explain how you can use the procedure in Activities and to find the volue of each rectangular pris. Then find the volue of each pris. a. b.. You have used the forulas V = Bh and V = wh to find the volue V of a rectangular pris with whole nuber edge lengths. Do you think the forulas work for rectangular priss with fractional edge lengths? Give exaples with your answer.. IN YOUR OWN WORDS How can you find the volue of a rectangular pris with fractional edge lengths? Use what you learned about the volue of a rectangular pris to coplete Exercises 6 on page. Section. Volues of Rectangular Priss
3 . Lesson Lesson Tutorials Key Vocabulary volue, p. Volue of a Rectangular Pris Words The volue V of a rectangular pris is the product of the area of the base and the height of the pris. Algebra V = Bh or V = wh length, area of base, B height, h width, w EXAMPLE Finding Volues of Rectangular Priss Find the volue of each pris. Study Tip In Exaple (b), the rectangular pris is a cube. You can use the forula V = s to find the volue V of a cube with an edge length of s. a. b. V = wh Write forula. V = wh = ( ) ( ) Substitute values. = ( ) ( ) = Multiply. = = So, the volue is So, the volue is cubic eter. cubic inches. Exercises 9 Find the volue of the pris... ft yd ft ft yd yd 6 Chapter Surface Area and Volue
4 EXAMPLE Using the Volue of a Rectangular Pris One cubic foot of dirt weighs about 0 pounds. How any pounds of dirt can the dup truck haul when it is full? ft ft ft Find the volue of dirt that the dup truck can haul when it is full. V = wh ) = () ( = 66 Multiply. Write forula for volue. Substitute values. So, the dup truck can haul 66 cubic feet of dirt when it is full. 0 lb To find the weight of the dirt, ultiply by ft. 66 ft 0 lb =,0 lb ft The dup truck can haul about,0 pounds of dirt when it is full. EXAMPLE h 6 Volue = 9 Finding a Missing Diension of a Rectangular Pris Write and solve an equation to find the height of the coputer tower. V = wh Write forula for volue. 9 = 6()h Substitute values. 9 = h Siplify. 9 = h 6 = h Siplify. Division Property of Equality So, the height of the coputer tower is 6 inches. Exercises 0. WHAT IF? In Exaple, the length of the dup truck is 0 feet. How any pounds of dirt can the dup truck haul when it is full? Write and solve an equation to find the issing diension of the pris.. Volue =. Volue = 6 w 0 Section. Volues of Rectangular Priss
5 Exercises. Help with Hoework. CRITICAL THINKING Explain how volue and surface area are different.. REASONING Will the forulas for volue work for rectangular priss with decial edge lengths? Expla. DIFFERENT WORDS, SAME QUESTION Which is different? Find both answers. How uch does it take to fill the rectangular pris? 0 What is the capacity of the rectangular pris? How uch does it take to cover the rectangular pris? How uch does the rectangular pris contain? 6)= 9+(- )= +(- 9)= +(- = ) 9+(- Find the volue of the pris.... ft 6. ft. 9. ft 6 Write and solve an equation to find the issing diension of the pris. 0. Volue = 60. Volue = 0. h 9 TieKeeper 9 Chapter s_green pe_00.indd Volue = w w 9 Surface Area and Volue // :: PM
6 . FISH TANK One cubic foot of water weighs about 6. pounds. How any pounds of water can the fish tank hold when it is full?. CUBE How any -centieter cubes do you need to create a cube with an edge length of centieters?. ft ft. ft. REASONING How any -inch cubes do you need to fill a cube that has an edge length of foot? How can this result help you convert a volue fro cubic inches to cubic feet? fro cubic feet to cubic inches? 6. FOOD STORAGE a. Estiate the aount of casserole left in the dish. b. Will the casserole fit in the storage container? Explain your reasoning.. PROBLEM SOLVING The area of the shaded face is 96 square centieters. What is the volue of the rectangular pris?. You have 00 square feet of boards to use for a new tree house. a. Design a tree house that has a volue of at least 0 cubic feet. Include sketches of your tree house. b. Are your diensions reasonable? Explain your reasoning. Tell whether the given value is a solution of the equation. (Section.) 9. x + = ; x = 0. x = 6; x =. x 9 = ; x =. MULTIPLE CHOICE Which set of integers is ordered fro least to greatest? (Section 6.) A,,,, B,,,, C,,,, 0 D, 9, 6,, Section. Volues of Rectangular Priss 9
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