Question

writing the volume as an algebraic expression a right pyramid with a square base has a base length of x inches, and the height is two inches longer than the length of the base. which expression represents the volume in terms of x? \\(\frac{x^2(x + 2)}{3}\\) cubic inches \\(\frac{x(x + 2)}{3}\\) cubic inches \\(\frac{x^3}{3}+2\\) cubic inches \\(\frac{x^3 + 2}{3}\\) cubic inches

Explanation:

Step1: Recall pyramid volume formula

The volume $V$ of a pyramid is $V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$

Step2: Calculate square base area

Base is a square with side $x$, so area $= x^2$

Step3: Identify pyramid height

Height is $x+2$ inches

Step4: Substitute into volume formula

$V = \frac{1}{3} \times x^2 \times (x+2) = \frac{x^2(x+2)}{3}$

Answer:

$\frac{x^2(x+2)}{3}$ cubic inches