Question

what is the approximate surface area of an aa battery? 49.5 mm 14 mm a. 2,485 mm² b. 5,583 mm² c. 2,176 mm² d. 1,242 mm²

Explanation:

Step1: Identify the shape of the battery

An AA - battery is a cylinder. The formula for the surface area of a cylinder is $S = 2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Calculate the radius

Given the diameter $d = 14$ mm, then the radius $r=\frac{d}{2}=\frac{14}{2}=7$ mm, and the height $h = 49.5$ mm.

Step3: Calculate the two - base area

The area of the two bases is $2\pi r^2=2\times\pi\times7^2=2\times\pi\times49 = 98\pi$ mm².

Step4: Calculate the lateral area

The lateral area is $2\pi rh=2\times\pi\times7\times49.5 = 693\pi$ mm².

Step5: Calculate the total surface area

$S=98\pi + 693\pi=791\pi\approx791\times3.14 = 2483.74\approx2485$ mm².

Answer:

A. $2,485$ mm²