Question

a solid right pyramid has a square base. the base edge length is 2 cm longer than the height of the pyramid. if the height is 6 cm, what is the volume of the pyramid?

\\(24\text{ cm}^3\\)
\\(48\text{ cm}^3\\)
\\(128\text{ cm}^3\\)
\\(144\text{ cm}^3\\)

Explanation:

Determine the base edge length

Using the Pyramid Base Geometry knowledge point

$$
LATEXBLOCK0
$$

Calculate the base area

Using the Pyramid Base Geometry knowledge point

$$ B = s^2 = 8^2 = 64\text{ cm}^2 $$

Calculate the volume of the pyramid

Using the Volume of a Right Pyramid knowledge point

$$ V = \frac{1}{3} \cdot B \cdot h = \frac{1}{3} \cdot 64 \cdot 6 = 128\text{ cm}^3 $$

Answer:

• (A) \(24\text{ cm}^3\)
• (B) \(48\text{ cm}^3\)
• (C) \(128\text{ cm}^3\) (Correct answer)
• (D) \(144\text{ cm}^3\)