Question

the oblique pyramid has a square base.
what is the volume of the pyramid?

• 2.5 cm^3
• 5 cm^3
• 6 cm^3
• 7.5 cm^3

Explanation:

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"concepts_used": [
"Pyramid Base Geometry",
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<reasoning>

Calculate the area of the square base

Using the Pyramid Base Geometry knowledge point
\[

$$\begin{aligned} s &= 2\text{ cm} \\ B &= s^2 = 2^2 = 4\text{ cm}^2 \end{aligned}$$

\]

Calculate the volume of the oblique pyramid

Using the Volume of Oblique Pyramids knowledge point
\[

$$\begin{aligned} h &= 3.75\text{ cm} \\ V &= \frac{1}{3} \cdot B \cdot h = \frac{1}{3} \cdot 4 \cdot 3.75 = 5\text{ cm}^3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 2.5 cm³</mcq-option>
<mcq-correct>(B) 5 cm³</mcq-correct>
<mcq-option>(C) 6 cm³</mcq-option>
<mcq-option>(D) 7.5 cm³</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
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"Volume of Oblique Pyramids"
]
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</post_analysis>

Answer:

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}
</pre_analysis>

<reasoning>

Calculate the area of the square base

Using the Pyramid Base Geometry knowledge point
\[

$$\begin{aligned} s &= 2\text{ cm} \\ B &= s^2 = 2^2 = 4\text{ cm}^2 \end{aligned}$$

\]

Calculate the volume of the oblique pyramid

Using the Volume of Oblique Pyramids knowledge point
\[

$$\begin{aligned} h &= 3.75\text{ cm} \\ V &= \frac{1}{3} \cdot B \cdot h = \frac{1}{3} \cdot 4 \cdot 3.75 = 5\text{ cm}^3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 2.5 cm³</mcq-option>
<mcq-correct>(B) 5 cm³</mcq-correct>
<mcq-option>(C) 6 cm³</mcq-option>
<mcq-option>(D) 7.5 cm³</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
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"Volume of Oblique Pyramids"
]
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