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:

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:

$$V = B \times h$$

$$V = 25\text{ in}^2 \times 10\text{ in} = 250\text{ in}^3$$

Answer:

• (A) \(150\text{ in}^3\)
• (B) \(200\text{ in}^3\)
• (C) \(250\text{ in}^3\) (Correct answer)
• (D) \(300\text{ in}^3\)