Final answer:
The surface area of the cylinder with a height of 5 inches and a radius of 3 inches is calculated using the formula A = 2πrh + 2πr² and comes out to approximately 150.796 in² when rounded to the nearest thousandth.
Step-by-step explanation:
To calculate the surface area of a cylinder, we use the formula A = 2πrh + 2πr², where 'r' is the radius and 'h' is the height of the cylinder. Given the height 'h' is 5 inches and the radius 'r' is 3 inches, we substitute these values into the formula.
Calculating the lateral surface area (the area of the side):
A_lateral = 2πrh = 2π(3 in)(5 in) = 30π in².
Calculating the area of the two bases:
A_bases = 2πr² = 2π(3 in)² = 18π in².
Now, add the lateral area and the area of the bases to find the total surface area:
A_total = A_lateral + A_bases = 30π in² + 18π in² = 48π in².
Using π ≈ 3.14159, the total surface area is: A_total ≈ 48(3.14159) = 150.796 in². Rounded to the nearest thousandth, the surface area of the cylinder is 150.796 in².