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Example 6

Example 6. Solve a multi-step problem. TERRARIUM.

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Example 6

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  1. Example 6 Solve a multi-step problem TERRARIUM A large terrarium is used to display a box turtle in a pet store. The terrarium has the shape of a rectangular prism with a volume of 8748 cubic inches. The dimensions of the terrarium are shown. Find the length, width, and height of the terrarium.

  2. Example 6 SOLUTION STEP 1 Write a verbal model. Then write an equation. 8748 w 36 w w 9 + ( ) ( ) – = • • ( ) Write equation. 8748 w 36 = + – – w3 Multiply. Subtract 8748 from each side. 0 27w2 324w 8748 + = ( ) w ( ) – w 9 Solve a multi-step problem STEP 2 Solve the equation for w.

  3. Example 6 ) ( – 0 = 324w + 8748 Group terms. Factor each group. ( ) ( ) – = w2 w + 27 0 324 w 27 + ( ) ( ) 0 – = w2 324 w 27 Distributive property + ( ) w 27 + Difference of two squares pattern 0 = ( ) – w 18 w 18 = or or Zero-product property w 18 0 w – 18 0 w 27 0 + + = = = ( ) w 18 + or or Solve for w. – – w 18 w 18 w 27 = = = Because the width cannot be negative, the only solution is ) ( w3 + 27w2 Solve a multi-step problem

  4. Example 6 Length Height ANSWER = = 54 w + 36 18 + 36 – – = w 9 = 18 9 = 9 The length is 54 inches, the width is 18 inches, and the height is 9 inches. Solve a multi-step problem STEP 3 Find the length and height.

  5. Guided Practice 13. DIMENSIONS OF A BOX A box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of feet, and a height of feet. Find the dimensions of the box. 3 ftlong by2ftwide by12fthigh ANSWER ( ) ( ) – x 9 x 1 + for Example 6

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