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?

• $3x^2$ cm³
• $9x^2$ cm³
• $3x$ cm³
• $x$ cm³

Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.

Step2: Find the area of the base

The base is a square with edge length \( x \) cm, so the area of the base \( B = x\times x=x^{2}\text{ cm}^2 \).

Step3: Substitute the base area and height into the volume formula

The height \( h = 9 \) cm. Substituting \( B = x^{2} \) and \( h = 9 \) into \( V=\frac{1}{3}Bh \), we get \( V=\frac{1}{3}\times x^{2}\times9 \).
Simplifying \( \frac{1}{3}\times9 = 3 \), so \( V = 3x^{2}\text{ cm}^3 \).

Answer:

\( 3x^{2}\text{ cm}^3 \) (corresponding to the option " \( 3x^{2}\text{ cm}^3 \)")