Final Answer:
The expression that represents the volume of the cylinder in cubic units is A) 40x². Therefore, The correct option is A) 40x² because it aligns with the formula for the volume of a cylinder, where the volume (V) is proportional to the square of the radius (x²). The expression A) 40x² indicates a constant factor (40) multiplied by the squared radius (x²), which corresponds to the standard formula for the volume of a cylinder, validating its correctness in this context.
Step-by-step explanation:
The volume V of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height. In this case, the expression A) 40x² can be interpreted as 40 times x squared. To align this with the cylinder volume formula, we can consider x as the radius and 40 as a constant multiplier. Therefore, the expression can be written as V = 40πx², which matches the form of the cylinder volume formula.
Now, let's delve into the details of the calculation. The expression 40x² indicates that the cylinder has a constant factor of 40 and the variable x squared. In the context of a cylinder, x would represent the radius. So, when you square the radius (x²) and multiply it by the constant factor (40), you get the expression for the volume of the cylinder. This aligns with the formula for the volume of a cylinder, confirming that option A) is the correct representation.
In summary, the expression A) 40x² corresponds to the correct mathematical representation of the volume of a cylinder, where 40 is a constant multiplier and x² represents the squared radius. Thus, A) 40x² is the accurate choice for the volume of the cylinder in cubic units.