An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base. The surface area of the metallic sheet used is equal to curved surface area of frustum + area of circular base + curved surface area of cylinder.
Step 1: The bucket is said to be open. This means there is no metallic sheet used at the top, so we do not count the top circular area.
Step 2: The frustum (truncated cone) has a curved surface area. This part of the metal sheet is used, so we must include it.
Step 3: The frustum is fixed onto a hollow cylindrical base. The cylinder also has a curved surface area, and that part is also made of metal, so it must be included.
Step 4: The bucket has a bottom circular base (the base of the cylinder). This also requires metal, so its area must be added.
Step 5: Total metallic sheet used = Curved Surface Area of frustum + Curved Surface Area of cylinder + Area of bottom circular base.
Step 6: This matches exactly with the statement in the question.
Therefore, the statement is true.
Note: All areas are measured in square metres (m²) in SI units.