the base of a solid right pyramid is a square with an edge length of $n$ units. the height of the pyramid is $n - 1$ units. which expression represents the volume of the pyramid?

$\frac{1}{3}n(n - 1)\text{ units}^3$
$\frac{1}{3}n(n - 1)^2\text{ units}^3$
$\frac{1}{3}n^2(n - 1)\text{ units}^3$
$\frac{1}{3}n^3(n - 1)\text{ units}^3$

Question

the base of a solid right pyramid is a square with an edge length of $n$ units. the height of the pyramid is $n - 1$ units. which expression represents the volume of the pyramid?

$\frac{1}{3}n(n - 1)\text{ units}^3$
$\frac{1}{3}n(n - 1)^2\text{ units}^3$
$\frac{1}{3}n^2(n - 1)\text{ units}^3$
$\frac{1}{3}n^3(n - 1)\text{ units}^3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Volume of a Pyramid" ], "new_concepts": [], "current_concepts": [ "Volume of a Pyramid" ] } ## Calculate the base area of the square pyramid $$ B = n^2 $$ ## Apply the pyramid volume formula $$ \begin{aligned} V &= \frac{1}{3} \cdot B \cdot h \ V &= \frac{1}{3} n^2 (n - 1) \end{aligned} $$

(A) $\frac{1}{3}n(n - 1)\text{ units}^3$

(B) $\frac{1}{3}n(n - 1)^2\text{ units}^3$

(C) $\frac{1}{3}n^2(n - 1)\text{ units}^3$

(D) $\frac{1}{3}n^3(n - 1)\text{ units}^3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Pyramid" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the base area of the square pyramid

Apply the pyramid volume formula

Answer: