Question

1. (06.02 mc)

a watch company is developing packaging for its new watch. the designer uses hexagons with a base area of \\(25\text{ in}^2\\) and rectangles with a length of \\(10\text{ in}\\) to create a prototype for the new package. what is the volume of the prototype? (1 point)

• \\(150\text{ in}^3\\)
• \\(200\text{ in}^3\\)
• \\(250\text{ in}^3\\)
• \\(300\text{ in}^3\\)

Explanation:

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<reasoning>

Identify the geometric solid

The packaging prototype is constructed using hexagons as bases and rectangles as lateral faces, which forms a right hexagonal prism.

Determine the given parameters

The base area \(B\) of the hexagonal base is:
\[B = 25\text{ in}^2\]
The length of the rectangles represents the height \(h\) of the prism:
\[h = 10\text{ in}\]

Calculate the volume

The volume \(V\) of a prism is calculated by multiplying the base area by the height:
\[V = B \times h\]
\[V = 25\text{ in}^2 \times 10\text{ in} = 250\text{ in}^3\]
</reasoning>

<answer>
<mcq-option>(A) \(150\text{ in}^3\)</mcq-option>
<mcq-option>(B) \(200\text{ in}^3\)</mcq-option>
<mcq-correct>(C) \(250\text{ in}^3\)</mcq-correct>
<mcq-option>(D) \(300\text{ in}^3\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the geometric solid

The packaging prototype is constructed using hexagons as bases and rectangles as lateral faces, which forms a right hexagonal prism.

Determine the given parameters

The base area \(B\) of the hexagonal base is:
\[B = 25\text{ in}^2\]
The length of the rectangles represents the height \(h\) of the prism:
\[h = 10\text{ in}\]

Calculate the volume

The volume \(V\) of a prism is calculated by multiplying the base area by the height:
\[V = B \times h\]
\[V = 25\text{ in}^2 \times 10\text{ in} = 250\text{ in}^3\]
</reasoning>

<answer>
<mcq-option>(A) \(150\text{ in}^3\)</mcq-option>
<mcq-option>(B) \(200\text{ in}^3\)</mcq-option>
<mcq-correct>(C) \(250\text{ in}^3\)</mcq-correct>
<mcq-option>(D) \(300\text{ in}^3\)</mcq-option>
</answer>

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