find the height of a pyramid with a volume of $128\text{ cm}^3$ if the base is a square with a side length of $8\text{ cm}$.

$\quad\text{ cm}$

Question

find the height of a pyramid with a volume of $128\text{ cm}^3$ if the base is a square with a side length of $8\text{ cm}$.

$\quad\text{ cm}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Volume of a Square Pyramid" ], "new_concepts": [], "current_concepts": [ "Volume of a Square Pyramid" ] } ## Identify given values and formula $$ \begin{aligned} &V = 128\text{ cm}^3\ &s = 8\text{ cm}\ &V = \frac{1}{3} \cdot B \cdot h = \frac{1}{3} \cdot s^2 \cdot h \end{aligned} $$ ## Calculate base area $$ B = s^2 = 8^2 = 64\text{ cm}^2 $$ ## Solve for height $$ \begin{aligned} 128 &= \frac{1}{3} \cdot 64 \cdot h\ 2 &= \frac{1}{3} \cdot h\ h &= 6\text{ cm} \end{aligned} $$ Find the height of a pyramid with a volume of $128\text{ cm}^3$ if the base is a square with a side length of $8\text{ cm}$. 6 cm { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Square Pyramid" ] }

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Question

Explanation:

Identify given values and formula

Calculate base area

Solve for height

Answer: