Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 2 cm 14 cm what is the area of the rectangle? hint: rectangle length = circumference both circles: 25.12 cm² rectangle: ?cm² total sa: cm²

Explanation:

Step1: Calculate the circumference of the base

The formula for the circumference of a circle is $c = 2\pi r$. Given $r = 2$ cm and $\pi=3.14$, we have $c=2\times3.14\times2= 12.56$ cm.

Step2: Calculate the area of the rectangle

The area of the rectangle in the cylinder's net is $A_{rect}=c\times h$. Here, $h = 14$ cm and $c = 12.56$ cm, so $A_{rect}=12.56\times14 = 175.84$ $cm^{2}$.

Step3: Calculate the area of the two - circular bases

The formula for the area of a circle is $A=\pi r^{2}$. For two bases, $A_{bases}=2\times\pi r^{2}$. Substituting $r = 2$ cm and $\pi = 3.14$, we get $A_{bases}=2\times3.14\times2^{2}=2\times3.14\times4 = 25.12$ $cm^{2}$.

Step4: Calculate the total surface area of the cylinder

The total surface area of a cylinder $SA=A_{rect}+A_{bases}$. So $SA=175.84 + 25.12=200.96$ $cm^{2}$.

Answer:

$200.96$ $cm^{2}$