Question

Give me a word problem to match (12x2)+(4x3)

Answer 1

The expression
`\(12x^2 + 4x^3\)` represents the total volume of a rectangular prism sculpture. The term
`\(12x^2\)` accounts for the base volume, and
`\(4x^3\)` represents the added volume of an extra layer on top, providing a model for calculating the total volume.

Let's consider a word problem that can be modeled by the expression
`\(12x^2 + 4x^3\)`. Imagine a rectangular prism with sides of length x and a rectangular base. The expression represents the total volume of the prism, where
`\(12x^2\)` corresponds to the volume of the rectangular base, and
`\(4x^3\)` represents the volume of an additional rectangular layer stacked on top.

Suppose you are building a sculpture using identical rectangular prisms. The base of each prism has an area of
`\(12x^2\)` square units, and each prism is x units tall. The sculptor decides to add an extra layer to the top of each prism, increasing the height by x units. The expression
`\(4x^3\)` represents the additional volume of the top layer for each prism. Therefore, the entire expression
`\(12x^2 + 4x^3\)` gives the total volume of one prism with the added layer, and you can use it to calculate the total volume for a given number of prisms.