Question

the base edge of an oblique square pyramid is represented as x cm. if the height is 9 cm, what is the volume of the pyramid in terms of x?
$\bigcirc$ $3x^2\\ \mathrm{cm}^3$
$\bigcirc$ $9x^2\\ \mathrm{cm}^3$
$\bigcirc$ $3x\\ \mathrm{cm}^3$
$\bigcirc$ $x\\ \mathrm{cm}^3$

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 base area

The base is a square with edge $x$, so area $= x^2$

Step3: Substitute values into formula

Substitute base area $x^2$ and height $9$:
$V = \frac{1}{3} \times x^2 \times 9$

Step4: Simplify the expression

$V = 3x^2$

Answer:

$3x^2$ cm³ (Option A)