Question

evaluate the expression for the given value of the variable. use 3.14 for \\(\pi\\). round the answer to the nearest hundredth when necessary.

\\\frac{1}{3} \pi r^2 \text{ for } r = 8\\

\\\frac{1}{3} \pi r^2 = \boxed{\phantom{x}}\\

Explanation:

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<reasoning>

Substitute the given values into the expression

\[
\frac{1}{3}\pi r^2 = \frac{1}{3} \cdot 3.14 \cdot 8^2
\]

Simplify the exponent and multiply

\[
\frac{1}{3} \cdot 3.14 \cdot 64 = \frac{200.96}{3}
\]

Divide and round to the nearest hundredth

\[
\frac{200.96}{3} \approx 66.98667 \approx 66.99
\]
</reasoning>

<answer>
Evaluate the expression for the given value of the variable. Use 3.14 for \(\pi\). Round the answer to the nearest hundredth when necessary.

\(\frac{1}{3}\pi r^2 =\) <blank>66.99</blank>
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Algebraic Evaluation"
]
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Answer:

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</pre_analysis>

<reasoning>

Substitute the given values into the expression

\[
\frac{1}{3}\pi r^2 = \frac{1}{3} \cdot 3.14 \cdot 8^2
\]

Simplify the exponent and multiply

\[
\frac{1}{3} \cdot 3.14 \cdot 64 = \frac{200.96}{3}
\]

Divide and round to the nearest hundredth

\[
\frac{200.96}{3} \approx 66.98667 \approx 66.99
\]
</reasoning>

<answer>
Evaluate the expression for the given value of the variable. Use 3.14 for \(\pi\). Round the answer to the nearest hundredth when necessary.

\(\frac{1}{3}\pi r^2 =\) <blank>66.99</blank>
</answer>

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"question_type": "Fill-in-the-blank",
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"Mathematics",
"Algebra",
"Algebraic Evaluation"
]
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