Question

Using v = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown. The height is (2d - 6)/(2d - 4). The width is 4/(d - 4). The length is (d - 2)/(3d - 9).

1) 4(d - 2)/(3(d - 3)(d - 4))
2) 4(d - 8)/(3(d - 4)²)
3) 4/(3d - 12)
4) 1/(3d - 3)

Answer 1

The volume of the prism with the given dimensions is found by multiplying the simplified expressions of length, width, and height and using V = lwh. After simplifications and cancellations, the correct expression for volume is option 1: 4(d - 2)/(3(d - 3)(d - 4)).

Step-by-step explanation:

We are given a prism with height (2d - 6)/(2d - 4), width 4/(d - 4), and length (d - 2)/(3d - 9). To find the volume of the prism, we will use the formula V = lwh.

First, let's simplify the given dimensions. Observe that the length has a common factor in the numerator and the denominator, so we can simplify:

• Length: (d - 2)/(3d - 9) = (d - 2)/3(d - 3)
• Width: 4/(d - 4)
• Height: (2d - 6)/(2d - 4) = 2(d - 3)/2(d - 2) = (d - 3)/(d - 2) after canceling the factor of 2.

Now we will multiply these expressions to get the volume:

V = (d - 2)/3(d - 3) × 4/(d - 4) × (d - 3)/(d - 2)

The (d - 3) and (d - 2) terms cancel out, leaving:

V = 4/(3(d - 4))

So the correct expression for the volume is 4(d - 2)/(3(d - 3)(d - 4)), which is option 1.