Answer:
1206 square centimeters
Step-by-step explanation:
Hello, I can help you with that
a tin is a cylinder,a cylinder is formed by 2 circles anda 1 rectangle
let's remember
Area of the circle
![A=\pi *radius^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20%2Aradius%5E%7B2%7D)
Area of the rectangle
![A_{r}=length *wide\\](https://tex.z-dn.net/?f=A_%7Br%7D%3Dlength%20%2Awide%5C%5C)
the length of the rectangle is the height of the tin (16 cm)
and the wide is equal to the perimeter of the circle
perimeter of the circle(P)
![P=2*\pi *radius](https://tex.z-dn.net/?f=P%3D2%2A%5Cpi%20%2Aradius)
so, the area of the rectangle is
![A_{r}=length *wide\\\\A_{r}=heigth *2*\pi *radius](https://tex.z-dn.net/?f=A_%7Br%7D%3Dlength%20%2Awide%5C%5C%5C%5CA_%7Br%7D%3Dheigth%20%2A2%2A%5Cpi%20%2Aradius)
Step one
find the total area:
the total area is equal to 2 circles + 1 rectangle
![A_{total}=(2* \pi *radius^{2} )+(height*2*\pi *radius)](https://tex.z-dn.net/?f=A_%7Btotal%7D%3D%282%2A%20%5Cpi%20%2Aradius%5E%7B2%7D%20%29%2B%28height%2A2%2A%5Cpi%20%2Aradius%29)
Step two
put the values into the equation
height = 16 cm
radius= 8 cm
![A_{total}=(2* \pi *radius^{2} )+(height*2*\pi *radius)\\A_{total}=(2* \pi )+(16*2*\pi *8)\\A_{total}=(128* \pi )+(256*\pi )\\A_{total}= 378 \pi\\ A_{total}=1206.37](https://tex.z-dn.net/?f=A_%7Btotal%7D%3D%282%2A%20%5Cpi%20%2Aradius%5E%7B2%7D%20%29%2B%28height%2A2%2A%5Cpi%20%2Aradius%29%5C%5CA_%7Btotal%7D%3D%282%2A%20%5Cpi%20%20%29%2B%2816%2A2%2A%5Cpi%20%2A8%29%5C%5CA_%7Btotal%7D%3D%28128%2A%20%5Cpi%20%20%29%2B%28256%2A%5Cpi%20%29%5C%5CA_%7Btotal%7D%3D%20378%20%5Cpi%5C%5C%20A_%7Btotal%7D%3D1206.37)
so, the total area is 1206.37 square centimeters
I hope it helps, have a great day.