Question

1. (06.02 mc)

the circumference of a redwood tree trunk is \\(20\pi\text{ ft}\\), and it is \\(100\text{ ft}\\) tall. what is the approximate volume of the redwood tree trunk? (1 point)

\\(1,000\pi\text{ ft}^3\\)

\\(10,000\pi\text{ ft}^3\\)

\\(4,000\pi\text{ ft}^3\\)

\\(40,000\pi\text{ ft}^3\\)

Explanation:

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<reasoning>

Find the radius of the tree trunk

Using the Volume of Cylinders knowledge point
\[

$$\begin{aligned} C &= 2\pi r \\ 20\pi &= 2\pi r \\ r &= 10\text{ ft} \end{aligned}$$

\]

Calculate the volume of the cylinder

Using the Volume of Cylinders knowledge point
\[

$$\begin{aligned} V &= \pi r^2 h \\ V &= \pi (10)^2 (100) \\ V &= 10,000\pi\text{ ft}^3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(1,000\pi\text{ ft}^3\)</mcq-option>
<mcq-correct>(B) \(10,000\pi\text{ ft}^3\)</mcq-correct>
<mcq-option>(C) \(4,000\pi\text{ ft}^3\)</mcq-option>
<mcq-option>(D) \(40,000\pi\text{ ft}^3\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Find the radius of the tree trunk

Using the Volume of Cylinders knowledge point
\[

$$\begin{aligned} C &= 2\pi r \\ 20\pi &= 2\pi r \\ r &= 10\text{ ft} \end{aligned}$$

\]

Calculate the volume of the cylinder

Using the Volume of Cylinders knowledge point
\[

$$\begin{aligned} V &= \pi r^2 h \\ V &= \pi (10)^2 (100) \\ V &= 10,000\pi\text{ ft}^3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(1,000\pi\text{ ft}^3\)</mcq-option>
<mcq-correct>(B) \(10,000\pi\text{ ft}^3\)</mcq-correct>
<mcq-option>(C) \(4,000\pi\text{ ft}^3\)</mcq-option>
<mcq-option>(D) \(40,000\pi\text{ ft}^3\)</mcq-option>
</answer>

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