Question

the volume of an oblique pyramid with a square base is \\(v\text{ units}^3\\) and the height is \\(h\text{ units}\\).

which expression represents the area of the base of the pyramid?

\\(\bigcirc\quad \frac{3v}{h}\text{ units}^2\\)
\\(\bigcirc\quad (3v - h)\text{ units}^2\\)
\\(\bigcirc\quad (v - 3h)\text{ units}^2\\)
\\(\bigcirc\quad \frac{v}{3h}\text{ units}^2\\)

Explanation:

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<reasoning>

State the volume formula for an oblique pyramid

Using the Volume of Oblique Pyramids knowledge point
\[
V = \frac{1}{3} \cdot B \cdot h
\]

Solve the literal equation for the base area B

Using the Literal Equations knowledge point
\[

$$\begin{aligned} 3V &= B \cdot h \\ B &= \frac{3V}{h} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{3V}{h}\text{ units}^2\)</mcq-correct>
<mcq-option>(B) \((3V - h)\text{ units}^2\)</mcq-option>
<mcq-option>(C) \((V - 3h)\text{ units}^2\)</mcq-option>
<mcq-option>(D) \(\frac{V}{3h}\text{ units}^2\)</mcq-option>
</answer>

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Answer:

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<reasoning>

State the volume formula for an oblique pyramid

Using the Volume of Oblique Pyramids knowledge point
\[
V = \frac{1}{3} \cdot B \cdot h
\]

Solve the literal equation for the base area B

Using the Literal Equations knowledge point
\[

$$\begin{aligned} 3V &= B \cdot h \\ B &= \frac{3V}{h} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{3V}{h}\text{ units}^2\)</mcq-correct>
<mcq-option>(B) \((3V - h)\text{ units}^2\)</mcq-option>
<mcq-option>(C) \((V - 3h)\text{ units}^2\)</mcq-option>
<mcq-option>(D) \(\frac{V}{3h}\text{ units}^2\)</mcq-option>
</answer>

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