Question

what is the area of a cross section of a cylinder that is sliced so that the cross section is parallel to each base? if necessary, use 3.14 for \\(\pi\\). image of a cylinder with height 25 cm and diameter 8 cm enter your answer in the box. round your answer to the nearest square centimeter. \\(\square\\) cm\\(^2\\)

Explanation:

Step1: Identify the shape of the cross - section

When a cylinder is sliced parallel to its bases, the cross - section is a circle. The diameter of the circular base (and thus the cross - section) is given as \(d = 8\) cm. To find the radius \(r\) of the circle, we use the formula \(r=\frac{d}{2}\).
So, \(r=\frac{8}{2}=4\) cm.

Step2: Calculate the area of the circle

The formula for the area of a circle is \(A = \pi r^{2}\). We are given that \(\pi\approx3.14\) and \(r = 4\) cm.
Substitute the values into the formula: \(A=3.14\times4^{2}\).
First, calculate \(4^{2}=16\). Then, \(A = 3.14\times16\).
\(3.14\times16 = 50.24\) \(cm^{2}\).

Answer:

\(50\) (If we round \(50.24\) to the nearest square centimeter, we get \(50\). However, if we consider more precise rounding, sometimes \(50.24\) is rounded to \(50\) or \(50.24\) can be considered as is, but based on the instruction to round to the nearest square centimeter, the answer is \(50\) (or \(50.24\) if we don't round down, but the problem says "round your answer to the nearest square centimeter", so \(50\) or \(50.24\) depending on interpretation. But following the calculation \(3.14\times16 = 50.24\), and rounding to the nearest whole number is \(50\).)

Wait, actually, \(3.14\times16=50.24\), and when rounding to the nearest square centimeter, \(50.24\approx50\) (or some might say \(50\) or \(50.24\) is already a decimal, but the problem says "nearest square centimeter", so the answer is \(50\) (or \(50.24\) if we don't round). But let's check the calculation again. The diameter is \(8\) cm, radius is \(4\) cm. Area of circle is \(\pi r^{2}\), with \(\pi = 3.14\), so \(3.14\times4^{2}=3.14\times16 = 50.24\), which rounds to \(50\) when rounded to the nearest whole number. So the answer is \(50\) (or \(50.24\) if we keep one decimal place, but the problem says "nearest square centimeter", so whole number, so \(50\)).