EXAMPLE 4 Solve a multi-step problem ICE SCULPTURES

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Solve a multi-step problem

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EXAMPLE 4 Solve a multi-step problem ICE SCULPTURES

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Presentation transcript:

EXAMPLE 4 Solve a multi-step problem ICE SCULPTURES 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?

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

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

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

EXAMPLE 4 Solve a multi-step problem The only reasonable solution is x = 2. The base of the mold is 2 feet by 2 feet. The height of the mold is 2 + 1 = 3 feet. ANSWER

GUIDED PRACTICE for Example 4 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 6 cubic feet. What are the dimensions of the mold? 7. Base side: 3 ft, height: 2 ft ANSWER