Final answer:
To find the cylinder's surface area, calculate the radius using the volume and height, then use it to find the area of the ends and side. The surface area equals 80π square feet.
Step-by-step explanation:
To calculate the surface area of a cylinder with a given volume, we must first find the radius of the base circle. Given the volume of the cylinder (75 π cubic feet) and the height (3 feet), we can use the volume formula for a cylinder, V = πr²h, where V is the volume, r is the radius, and h is the height. The formula can be rearranged to solve for the radius (r) by dividing both sides by πh:
r² = V/(πh) = 75π / (π × 3) = 25
Therefore, r = √25 = 5 feet. Now we can find the surface area of the cylinder, which is the sum of the areas of the two circular ends (2πr²) and the rectangular side (2πrh):
Surface Area = 2πr² + 2πrh = 2π × 5² + 2π × 5 × 3 = 2π × 25 + 2π × 5 × 3 = 50π + 30π = 80π
The surface area of the cylinder is 80π square feet.