A tin is a right circular cylinder with a diameter of 6 meters and a height of 10 meters. What is the surface area of this tin, in terms of pi?
the answer would be 78pi
To find the surface area of the tin, we need to add up the areas of all its surfaces.
A right circular cylinder has two circular bases and a curved surface.
To find the area of each circular base, we can use the formula for the area of a circle: A = πr^2, where r is the radius.
Given that the diameter of the tin is 6 meters, the radius would be half of that, so r = 6/2 = 3 meters.
The area of each circular base would be A_base = π(3^2) = π(9) = 9π square meters.
The curved surface of the tin can be unwrapped and flattened out to form a rectangle. The length of the rectangle would be equal to the circumference of the circular base, and the height of the rectangle would be equal to the height of the cylinder.
The circumference of a circle can be found using the formula: C = 2πr.
Since the diameter is 6 meters, the radius r would be 3 meters. So, the circumference C would be C = 2π(3) = 6π meters.
Therefore, the area of the curved surface would be A_curved_surface = C * h, where h is the height of the cylinder.
Given that the height of the tin is 10 meters, the area of the curved surface would be A_curved_surface = 6π * 10 = 60π square meters.
Now, to find the total surface area, we add up the areas of the bases and the curved surface:
Total surface area = 2(A_base) + A_curved_surface
= 2(9π) + 60π
= 18π + 60π
= 78π square meters.
Therefore, the surface area of the tin, in terms of pi, is 78π square meters.