Final answer:
The surface area of a cylinder with a radius of 4 cm and a height of 2 cm is 150.72 square centimeters, calculated using the approximation 3.14 for pi and the formula SA = 2πr^2 + 2πrh.
Step-by-step explanation:
To find the surface area of a cylinder, we need to calculate both the area of the circular ends and the area of the side that wraps around the cylinder. The formula for the surface area (SA) of a cylinder is SA = 2πr2 + 2πrh, where r is the radius and h is the height of the cylinder.
For a cylinder with a radius (r) of 4 cm and a height (h) of 2 cm, and using 3.14 as an approximation for pi (π), we use the following calculations:
- Calculate the area of the two circular ends: Aends = 2 × 3.14 × 4 cm2 = 100.48 cm2.
- Calculate the area of the side (which can be thought of as the area of a rectangle with height equal to the cylinder height and width equal to the circumference of the circle): Aside = 2 × 3.14 × 4 cm × 2 cm = 50.24 cm2.
- Add both areas together to get the total surface area: SA = 100.48 cm2 + 50.24 cm2 = 150.72 cm2.
Therefore, the surface area of the cylinder is 150.72 cm2.