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?

EXAMPLE 4

SOLUTION

STEP 1

4 = x2(x + 1)13

Write equation.

12 = x3 + x2 Multiply each side by 3 and simplify.

0 = x3 + x2 – 12 Subtract 12 from each side.

Solve a multi-step problem

Write an equation for the volume of the ice sculpture.

EXAMPLE 4

STEP 2

STEP 3

1 1 1 0 – 12

1 2 2

1 2 2 – 10

Solve a multi-step problem

+ , + , + , + ,+ , + 11

21

31

41

61

121

List the possible rational solutions:

Test possible solutions. Only positive x-values make sense.

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

STEP 4

EXAMPLE 4

2 1 1 0 – 12

2 6 121 3 6 0

↑ 2 is a solution.

Solve a multi-step problem

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