Question

a solid oblique pyramid has a square base with edges measuring x cm. the height of the pyramid is (x + 2) cm. which expression represents the volume of the pyramid?\\(\frac{x^{3}+2x^{2}}{3}\\) cm³\\(\frac{x^{2}+2x^{2}}{2}\\) cm³\\(\frac{x^{3}}{3}\\) cm³\\(\frac{x^{3}+2x^{2}}{2}\\) cm³

Explanation:

Step1: Find base area of square

The base is a square with side length $x$, so area is side squared.
$A = x^2$

Step2: Recall pyramid volume formula

Volume of a pyramid is $\frac{1}{3} \times$ base area $\times$ height.
$V = \frac{1}{3} \times A \times h$

Step3: Substitute values into formula

Substitute $A = x^2$ and $h = (x+2)$ into the formula.
$V = \frac{1}{3} \times x^2 \times (x+2)$

Step4: Expand the expression

Distribute $x^2$ across $(x+2)$ then multiply by $\frac{1}{3}$.
$V = \frac{1}{3}(x^3 + 2x^2) = \frac{x^3 + 2x^2}{3}$

Answer:

$\frac{x^3 + 2x^2}{3}$ cm³ (corresponding to the first option)