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Try, Check, and Revise and Write an Equation

A cube is a rectangular prism in which length, width, and height are the same. Given the volume of 17,576 mm 3 , you need to find the length, width, and height of the cube. Method 1 Try, Check, and Revise.

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Try, Check, and Revise and Write an Equation

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  1. A cube is a rectangular prism in which length, width, and height are the same. Given the volume of 17,576 mm3, you need to find the length, width, and height of the cube. Method 1 Try, Check, and Revise You know the relationship between the length, width, and height of a cube. Use that to test possible dimensions of the cube and see if they produce the desired volume. Organize the test results in a table. COURSE 2 LESSON 8-10 Try, Check, and Revise and Write an Equation The volume of a cube is 17,576 mm3. What is the length of each edge of the cube? 8-10

  2. l w h Volume Conclusion 14 14 14 14 • 14 • 14 = 2,744 Too low 42 42 42 42 • 42 • 42 = 74,088 Too high 34 34 34 34 • 34 • 34 = 39,304 Too high 24 24 24 24 • 24 • 24 = 13,824 Too low 26 26 26 26 • 26 • 26 = 17,576 COURSE 2 LESSON 8-10 Try, Check, and Revise and Write an Equation (continued) The length of each edge of the cube is 26 mm. 8-10

  3. s = the length of the cube The length, height, and width of the cube are equal. s = the width of the cube s = the height of the cube Method 2 Write an Equation Another way to solve this is to use the formula for the volume of a rectangular prism to write an equation. COURSE 2 LESSON 8-10 Try, Check, and Revise and Write an Equation (continued) 8-10

  4. l • w • h = VUse the volume formula. s • s • s = 17,576 Substitute. s3 = 17,576 Simplify. 3 3 s3 = 17,576 Take the cube root of each side. s = 26 Simplify. COURSE 2 LESSON 8-10 Try, Check, and Revise and Write an Equation (continued) The formula for the volume of a rectangular prism is V = lwh. You know the volume is 17,576 mm3. The length, width, and height of the cube are each 26 mm, so the length of each edge of the cube is 26 mm. 8-10

  5. To check the answer you can use the definition of a cube. The length, width, and height have to be equal. l = w = h = 26 Also, the volume has to equal 17,576 mm3. 26 • 26 • 26 = 17,576 The answer checks. COURSE 2 LESSON 8-10 Try, Check, and Revise and Write an Equation (continued) 8-10

  6. COURSE 2 LESSON 8-10 Try, Check, and Revise and Write an Equation Use Try, Check, and Revise or Write an Equation to solve the problem. 1. A triangular sign has an area of 972 cm2. Its base is 36 cm long. What is the height of the sign? 2. Jan has 19 bills worth a total of $87. How many $1 bills, $5 bills, and $10 bills does she have? 54 cm seven $1 bills, eight $5 bills, and four $10 bills 8-10

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