Final answer:
The surface area of a cylinder with a radius of 7 inches and height of 4 inches is approximately 483.89 square inches, calculated using the formula A = 2πrh + 2πr².
Step-by-step explanation:
The surface area of a cylinder can be calculated using the formula A = 2πrh + 2πr², where r is the radius and h is the height of the cylinder. For a cylinder with a radius of 7 inches and a height of 4 inches, the surface area would be A = 2π(7 in)(4 in) + 2π(7 in)².
Plugging in the values, you would calculate the area of the side (also known as the lateral surface area) and the area of the two ends (also known as the base areas) and then sum them up to get the total surface area.
Doing the math: A = 2π(7)(4) + 2π(7)² = 2π(28) + 2π(49) = 56π + 98π = 154π. Since π ≈ 3.14159, the approximate surface area is ≈ 154 × 3.14159 ≈ 483.89 square inches.