Question

the volume of this rectangular prism is 4x³. what does the coefficient 4 mean in terms of the problem?
a. the length of the prism is 4 units.
b. the length is 4 times the width.
c. the width is 4 times the height and the length.
d. the total volume of the prism is 4 cubic units.

Explanation:

Step1: Analyze the volume formula of a rectangular prism

The volume \(V\) of a rectangular prism is given by \(V=\text{length}\times\text{width}\times\text{height}\). Here, length \(l = 4x\), width \(w=x\), height \(h=x\). So \(V=(4x)\times(x)\times(x)=4x^{3}\).

Step2: Interpret the coefficient in the volume formula

In the formula \(V = 4x^{3}\), when comparing with the general form of a monomial \(ax^{n}\) (where \(a\) is the coefficient and \(n\) is the exponent), the coefficient \(a = 4\) represents the multiple of the product of the variables \(x\times x\times x\). Since length \(l = 4x\) (width \(w=x\), height \(h=x\)), the coefficient \(4\) means the length is \(4\) times the width.

Answer:

B. The length is 4 times the width.