Answer:
the surface area of the cylinder with height 6 cm and radius 8 cm is approximately 703.968 square centimeters.
Explanation:
The surface area of a cylinder can be found by adding the area of the circular bases and the lateral area (the area of the curved side).
The formula for the lateral area of a cylinder is given by: Lateral area = 2πrh, where r is the radius of the cylinder and h is the height.
The formula for the area of a circle is given by: Area = πr^2, where r is the radius of the circle.
Using these formulas and the given values, we can find the surface area of the cylinder:
Lateral area = 2πrh = 2π(8)(6) = 96π
Area of the circular base = πr^2 = π(8^2) = 64π
Total surface area = 2(Area of circular base) + Lateral area = 2(64π) + 96π = 224π
Rounding to the nearest thousandth, we get:
Total surface area ≈ 703.968 square centimeters
Therefore, the surface area of the cylinder with height 6 cm and radius 8 cm is approximately 703.968 square centimeters.