Find the surface area of the cylinder with a radius of 8 mm and a height of 13 mm Find the volume of the cylinder, in cubic millimeters. Round your answer to the nearest hundredth.
To find the surface area of the cylinder, we first need to find the lateral surface area and the total surface area.
The lateral surface area of a cylinder is given by the formula:
Lateral Surface Area = 2πrh
where r is the radius and h is the height of the cylinder.
Plug in the values:
Lateral Surface Area = 2 * π * 8 mm * 13 mm
Lateral Surface Area = 208π mm²
The total surface area of a cylinder is given by the formula:
Total Surface Area = 2πr(r + h)
where r is the radius and h is the height of the cylinder.
Plug in the values:
Total Surface Area = 2 * π * 8 mm(8 mm + 13 mm)
Total Surface Area = 392π mm²
Now, we can find the volume of the cylinder.
The volume of a cylinder is given by the formula:
Volume = πr²h
where r is the radius and h is the height of the cylinder.
Plug in the values:
Volume = π * (8 mm)² * 13 mm
Volume = 832π mm³
Therefore, the surface area of the cylinder is 208π mm² for the lateral surface area and 392π mm² for the total surface area. The volume of the cylinder is 832π mm³.