The volume of a cube is 17,576 mm3. What is the length

of each edge of the cube?

COURSE 2 LESSON 8-10COURSE 2 LESSON 8-10

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.

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.

Method 1 Try, Check, and Revise

8-10

Try, Check, and Revise and Write an Equation

(continued)

COURSE 2 LESSON 8-10COURSE 2 LESSON 8-10

The length of each edge of the cube is 26 mm.

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

l w h Volume Conclusion

8-10

Try, Check, and Revise and Write an Equation

(continued)

COURSE 2 LESSON 8-10COURSE 2 LESSON 8-10

The length, height, and width of the cube are equal.

s = the length of the cube

s = the width of the cube

s = the height of the cube

8-10

Try, Check, and Revise and Write an Equation

Another way to solve this is to use the formula for the volume of a

rectangular prism to write an equation.

Method 2 Write an Equation

(continued)

COURSE 2 LESSON 8-10COURSE 2 LESSON 8-10

The length, width, and height of the cube are each 26 mm, so

the length of each edge of the cube is 26 mm.

The formula for the volume of a rectangular prism is V = lwh.

You know the volume is 17,576 mm3.

l • w • h = V Use 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.

8-10

Try, Check, and Revise and Write an Equation

(continued)

COURSE 2 LESSON 8-10COURSE 2 LESSON 8-10

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.

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?

COURSE 2 LESSON 8-10COURSE 2 LESSON 8-10

54 cm

seven $1 bills, eight $5 bills, and four $10 bills

8-10

Try, Check, and Revise and Write an Equation