Given the cylinder such that the radius of the base is (r) = 6 in
Also, given that the height of the cylinder is (h) = 17 in.
We need to find the surface area of the cylinder.
We know that the surface area of the cylinder is given by the following equation.
SA = 2*area of the base + area of the side.
==> SA = 2*A1 + A2
Let us calculate the area of the base.
We know that the area of the circle = r^2*pi
==> A1 = 36*pi = 113.1 in^2
Now we need to find the area of the sides.
A2 = circumference of the base * h
= 2*pi*r * h
= 2*6*pi*17 = 204*pi = 640.9 in^2
Now we will substitute into the surface area.
SA = 2*A1 + A2
= 2*113.1 + 640.9
= 226.2 + 640.9 = 867.1 in^2 (approx.)
Then, the surface area of the cylinder is 867.1 in^2
The surface total area A of the cylinder is given by:
A = 2pirh+pir^2 = 2pir(r+h), where r = radius, h = height. 2pirh is the area of the curved surface of the cylinder and 2pir^2 = is the area of the top and and bottom circular surfaces of the cylinder.
We substitute radius r = 6 inches and height h = 17 inches in A = 2pir(r+h) = 2pi*6(6+17) = 12pi*23 = 276pi = 867.08 sq inches.
Therefore the total surface are of the cylinder = A = 867.07 sq in.