Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 3 cm 6 cm what is the area of the rectangle? hint: rectangle length = circumference both circles: 56.52 cm² rectangle: ?cm² total sa: ?cm²

Explanation:

Step1: Calculate the circumference of the base circle

$c = 2\pi r$, with $r = 3$ cm and $\pi=3.14$, so $c=2\times3.14\times3= 18.84$ cm.

Step2: Calculate the area of the rectangle

The area of the rectangle $A_{rectangle}=c\times h$, where $h = 6$ cm and $c = 18.84$ cm. So $A_{rectangle}=18.84\times6 = 113.04$ $cm^{2}$.

Step3: Calculate the total surface - area of the cylinder

The total surface - area of the cylinder $A = A_{rectangle}+A_{both - circles}$. Given $A_{both - circles}=56.52$ $cm^{2}$ and $A_{rectangle}=113.04$ $cm^{2}$, so $A=113.04 + 56.52=169.56$ $cm^{2}$.

Answer:

The area of the rectangle is $113.04$ $cm^{2}$, and the total surface area of the cylinder is $169.56$ $cm^{2}$.