Question

you have 240 cubic inches of clay with which to make a sculpture shaped as a rectangular prism. You want the width to be 4 inches less than the length and the height to be 2 inches more than 3 times the length. What should the dimensions of the sculpture be.

Answer 1

To find the dimensions of the sculpture, set up equations based on the given information and solve for x. The approximate dimensions of the sculpture are: Length: 5.52 inches, Width: 1.52 inches, Height: 18.56 inches.

Step-by-step explanation:

To find the dimensions of the sculpture, we can set up equations based on the given information:

Let the length of the sculpture be x inches.

The width is 4 inches less than the length, so the width is (x-4) inches.

The height is 2 inches more than 3 times the length, so the height is (3x+2) inches.

The formula to calculate the volume of a rectangular prism is: Volume = length x width x height.

Substituting the given dimensions into the equation, we have:

Volume = x(x-4)(3x+2)

Since we know that the volume is 240 cubic inches, we can solve for x:

x(x-4)(3x+2) = 240 cubic inches

By solving this equation, we find that x is approximately 5.52 inches.

Therefore, the dimensions of the sculpture should be approximately:

Length: 5.52 inches

Width: 1.52 inches

Height: 18.56 inches

Answer 2

Length=6, width=2, height=20. We can write a function to solve this problem. Suppose the length of the sculpture is x inches. Then the width is (x-4) inches, and the height (3x+2) inches. Their product is the volume of the clay: x*(x-4)*(3x+2)=240. Solve the equation, the only real answer is 6, so the length is 6 inches. Width is 6-4=2, and height is 3*6+2=20.