Question

2
select the correct answer.
sophia has unsharpened pencils that are 20 centimeters long. what is the approximate surface area of a pencil?
0.5 cm
a. 61 cm²
b. 60 cm²
c. 52 cm²
d. 16 cm²

Explanation:

Step1: Calculate the lateral surface area of the hexagonal - prism - shaped pencil

The formula for the lateral surface area of a prism is \(S = Ph\), where \(P\) is the perimeter of the base and \(h\) is the height (length) of the prism.
For a regular hexagon with side length \(a = 0.5\mathrm{cm}\), the perimeter \(P=6a\). So \(P = 6\times0.5=3\mathrm{cm}\), and \(h = 20\mathrm{cm}\). Then \(S_{lateral}=Ph=3\times20 = 60\mathrm{cm}^2\).
The area of the two bases of the hexagon is relatively small compared to the lateral surface area. If we assume the thickness of the pencil's core (the circular part in the base) is negligible for the approximation (since the problem asks for an approximate value and in multiple - choice questions with these values), we can approximate the surface area of the pencil as the lateral surface area.

Answer:

B. \(60\mathrm{cm}^2\)