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 the base - area formula

The base is a square with side - length \(x\) cm. The area of a square \(A = s^2\), so the base - area \(A=x^2\) \(cm^2\).

Step2: Recall the volume formula for a pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Ah\), where \(A\) is the base - area and \(h\) is the height. Here, \(A = x^2\) and \(h=(x + 2)\).

Step3: Substitute the values into the volume formula

\[

$$\begin{align*} V&=\frac{1}{3}\times x^2\times(x + 2)\\ &=\frac{x^2(x + 2)}{3}\\ &=\frac{x^{2}\times x+x^{2}\times2}{3}\\ &=\frac{x^{3}+2x^{2}}{3}\text{ cm}^3 \end{align*}$$

\]

Answer:

\(\frac{x^{3}+2x^{2}}{3}\text{ cm}^3\)