EXAMPLE 4

1. Some ice sculptures are made by filling a mold with water and then freezing it. You are making such an ice sculpture for a school dance. It is to be shaped like a pyramid with a height that is 1 foot greater than the length of each side of its square base. The volume of the ice sculpture is 4 cubic feet. What are the dimensions of the mold? EXAMPLE 4 Solve a multi-step problem ICE SCULPTURES

2. 1 4 = x2(x + 1) 3 EXAMPLE 4 Solve a multi-step problem SOLUTION Write an equation for the volume of the ice sculpture. STEP 1 Write equation. 12 = x3 + x2 Multiply each side by 3 and simplify. 0 = x3 + x2 – 12 Subtract 12 from each side.

3. List the possible rational solutions: 1 2 3 4 6 12 + , + , + , + ,+ , + 1 1 1 1 1 1 1 1 1 0 – 12 1 2 2 1 2 2 – 10 EXAMPLE 4 Solve a multi-step problem STEP 2 Test possible solutions. Only positive x-values make sense. STEP3

4. 2 1 1 0 – 12 2 6 12 1 3 6 0 ↑ 2is a solution. Check for other solutions. The other two solutions, which satisfy – 3 +i √15 x2 + 3x + 6 = 0, arex = and can be discarded because they are imaginary numbers. 2 EXAMPLE 4 Solve a multi-step problem STEP 4

5. ANSWER The only reasonable solution isx = 2. The base of themold is2feet by2feet. The height of the mold is2 + 1 = 3feet. Solve a multi-step problem EXAMPLE 4

6. 7. WHAT IF? In Example 4, suppose the base of the ice sculpture has sides that are 1 foot longer than the height. The volume of the ice sculpture is 6cubicfeet. What are the dimensions of the mold? ANSWER Base side: 3 ft, height: 2 ft for Example 4 GUIDED PRACTICE