Final answer:
The surface area of a cylinder with a base radius of 3 and a height of 8 is approximately 210 square units, after rounding to two significant figures.
Step-by-step explanation:
The surface area of a cylinder is calculated by adding the areas of the two circular bases to the area of the rectangle that wraps around the cylinder when it is 'unrolled'. For a cylinder with a base radius of 3 and a height of 8, the formula for the total surface area (SA) is:
SA = 2πr2 + 2πrh
Where π is approximately 3.1416, r is the radius of the cylinder, and h is the height. Inputting our values, we get:
SA = 2π(32) + 2π(3)(8) = 2π(9) + 2π(24) = 18π + 48π = 66π
So the surface area SA is: 66 × 3.1416 ≈ 207.346 square units. However, since our values were given with only one decimal or significant figure, we should appropriately round our answer to two significant figures:
SA ≈ 210 square units