Question

Which of the following formulas correctly represents the relationship between the volume (V) of a rectangular prism, the length (l), width (w), and height (h)?

a) V = l + w + h
b) V = l * w * h
c) V = l / w / h
d) V = l - w - h

Answer 1

The correct formula for the volume of a rectangular prism is V = l * w * h, where V is volume, l is length, w is width, and h is height. This formula is dimensionally consistent and accurately calculates the three-dimensional space the prism occupies. The correct option is B.

Step-by-step explanation:

The correct formula that represents the relationship between the volume (V) of a rectangular prism, the length (l), width (w), and height (h) is V = l * w * h.

The volume of a rectangular prism is calculated by multiplying the length by the width and then by the height. This is because the volume is a measure of how much three-dimensional space an object occupies, and for a rectangular prism, that space is found by considering all three dimensions. Option (b) V = l * w * h is, therefore, the correct answer and is dimensionally consistent as it represents the dimensions in terms of cubic units.

To further clarify, options (a), (c), and (d) are not correct. Adding lengths (a) would not give volume, dividing lengths (c) would not correctly calculate volume, and subtracting lengths (d) would not yield a meaningful volume measurement.