The area of a circle, given the circumference, is found using this formula:
A = C²/4π
Therefore,
A ≈ 451.93 cm²
Surface area of cylinder is given by area of circle + area of the rectangle that curved around the cylinder
Area of the base of the cylinder =
![\pi r^{2} = 8^{2} \pi =64 \pi](https://tex.z-dn.net/?f=%20%5Cpi%20r%5E%7B2%7D%20%3D%208%5E%7B2%7D%20%5Cpi%20%3D64%20%5Cpi%20)
Area of the cylinder 'wall' = width × length =
![12](https://tex.z-dn.net/?f=12)
×
![2r \pi](https://tex.z-dn.net/?f=2r%20%5Cpi%20)
=
![12](https://tex.z-dn.net/?f=12)
×
![16 \pi](https://tex.z-dn.net/?f=16%20%5Cpi%20)
=
![192 \pi](https://tex.z-dn.net/?f=192%20%5Cpi%20)
Note that the wall of the cylinder is in the shape of a rectangle. The width of the rectangle is the height of the cylinder. The length of the rectangle is the circumference of the circle base.
Surface area of cone is given by
![\pirl](https://tex.z-dn.net/?f=%20%5Cpirl)
where
![l](https://tex.z-dn.net/?f=l)
is the slanted height of the cone
SA of cone =
![\pi (8)(10)=80 \pi](https://tex.z-dn.net/?f=%20%5Cpi%20%288%29%2810%29%3D80%20%5Cpi%20)
Hence total painted surface area is
Volume of cone=1/3 times height times pir^2
v=15
r=3
15=1/3 hpi3^2
15=1/3hpi9
15=9/3hpi
15=3hpi
divide 3
5=hpi
h=5/pi
pi=aprox 3.14
5/3.14=1.59
1.59 ft