Question

if the volume of a cube is 8, what is the total surface area of the cube?

(a) 2
(b) 4
(c) 16
(d) 24
(e) 64

Explanation:

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<reasoning>

Identify the given volume

We are given that the volume of a cube is \(V = 8\).

Find the side length

The volume of a cube with side length \(s\) is given by:
\[V = s^3\]
We solve for \(s\):
\[s^3 = 8 \implies s = \sqrt[3]{8} = 2\]

Calculate the surface area

A cube has 6 identical square faces. The total surface area \(A\) is:
\[A = 6s^2\]
Substitute \(s = 2\) into the formula:
\[A = 6(2)^2 = 6(4) = 24\]
</reasoning>

<answer>
<mcq-option>(A) 2</mcq-option>
<mcq-option>(B) 4</mcq-option>
<mcq-option>(C) 16</mcq-option>
<mcq-correct>(D) 24</mcq-correct>
<mcq-option>(E) 64</mcq-option>
</answer>

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"knowledge_point": [
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Answer:

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</pre_analysis>

<reasoning>

Identify the given volume

We are given that the volume of a cube is \(V = 8\).

Find the side length

The volume of a cube with side length \(s\) is given by:
\[V = s^3\]
We solve for \(s\):
\[s^3 = 8 \implies s = \sqrt[3]{8} = 2\]

Calculate the surface area

A cube has 6 identical square faces. The total surface area \(A\) is:
\[A = 6s^2\]
Substitute \(s = 2\) into the formula:
\[A = 6(2)^2 = 6(4) = 24\]
</reasoning>

<answer>
<mcq-option>(A) 2</mcq-option>
<mcq-option>(B) 4</mcq-option>
<mcq-option>(C) 16</mcq-option>
<mcq-correct>(D) 24</mcq-correct>
<mcq-option>(E) 64</mcq-option>
</answer>

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