Question

the height of a right rectangular prism is 3 units greater than the length of the base. the edge length of the square base is x units. which expression represents the volume of the prism, in cubic units? \\(\bigcirc\\) \\(x^3 + 9\\) \\(\bigcirc\\) \\(x^3 + 3x^2\\) \\(\bigcirc\\) \\(x^3 + 3x + 3\\) \\(\bigcirc\\) \\(x^3 + 6x^2 + 9x\\)

Explanation:

Step1: Define base area

The base is a square with side $x$, so area is $x^2$.

Step2: Define prism height

Height = base length + 3, so $h = x+3$.

Step3: Calculate volume

Volume = base area × height:
$$V = x^2(x+3) = x^3+3x^2$$

Answer:

$x^3+3x^2$