Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 4 cm 9 cm what is the area of the rectangle? hint: rectangle length = circumference both circles: 100.48 cm² rectangle: ? cm² total sa: cm²

Explanation:

Step1: Calculate the circumference of the base circle

The formula for the circumference of a circle is $c = 2\pi r$. Given $r = 4$ cm and $\pi=3.14$, we have $c=2\times3.14\times4=25.12$ cm.

Step2: Calculate the area of the rectangle

The area of the rectangle in the cylinder - net is $A_{rectangle}=c\times h$, where $h = 9$ cm and $c = 25.12$ cm. So $A_{rectangle}=25.12\times9 = 226.08$ $cm^{2}$.

Step3: Calculate the total surface - area of the cylinder

The total surface - area of the cylinder $A = A_{rectangle}+A_{circles}$. Given $A_{circles}=100.48$ $cm^{2}$ and $A_{rectangle}=226.08$ $cm^{2}$, then $A=226.08 + 100.48=326.56$ $cm^{2}$.

Answer:

The area of the rectangle is $226.08$ $cm^{2}$ and the total surface - area of the cylinder is $326.56$ $cm^{2}$.