Final answer:
The surface area of the cylinder is approximately 0.029437 m².
Step-by-step explanation:
The surface area of a cylinder can be calculated using the formula:
A = 2πr² + 2πrh
where r is the radius of the cylinder and h is the height.
Given the information provided, we need to first calculate the volume of the cylinder using the formula V = πr²h. Using the given values, we have:
V = 3.142 × (0.750 cm)² × 5.25 cm = 9.278 cm³
Next, we can calculate the surface area using the formula A = 2πr² + 2πrh. Plugging in the values, we get:
A = 2π(0.750 cm)² + 2π(0.750 cm)(5.25 cm) = 4.712 cm² + 24.725 cm² = 29.437 cm²
Converting the units to meters, we have:
A = 29.437 cm² × (0.01 m/cm)² = 0.029437 m²
Therefore, the surface area of the cylinder is approximately 0.029437 m².