Final answer:
The internal volume of the vessel is approximately 381.7 cm³. The volume of the metal is approximately -205.8 cm³, but since it is negative, there may be an error in the calculations or the given measurements.
Step-by-step explanation:
a) The internal volume of the vessel:
The formula to calculate the volume of a cylinder is V = πr²h, where r is the radius and h is the height of the cylinder. In this case, the internal diameter is given, so we need to find the radius by dividing the diameter by 2. The internal height is already provided.
Therefore, the internal volume of the vessel can be calculated as follows:
V = π(7/2 cm)² × 10 cm
V ≈ 3.142 × (3.5 cm)² × 10 cm
V ≈ 3.142 × 12.25 cm² × 10 cm
V ≈ 381.7 cm³
b) The volume of the metal:
The external volume of the vessel can be calculated using the same formula as in part b, but using the external measurements (diameter + thickness and height). Then, subtract the internal volume calculated in part b to get the volume of the metal. Therefore, the volume of the metal can be calculated as follows:
Vmetal = Vexternal - Vinternal
Vmetal ≈ (3.142 × (7/2 + 1/2 cm)² × (10 + 1 cm)) - 381.7 cm³
Vmetal ≈ (3.142 × 4 cm² × 11 cm) - 381.7 cm³
Vmetal ≈ 175.9 cm³ - 381.7 cm³
Vmetal ≈ -205.8 cm³
Since the volume of the metal is negative, it means that there was an error in the calculations or the given measurements. Please double-check the measurements provided to ensure accuracy.