Answer:
Explanation:
To find the surface area of a cylinder, we need to add the area of the circular bases to the lateral area (the curved surface).
The diameter of the cylinder is 9 inches, so the radius (r) is half of that, or 4.5 inches.
The height of the cylinder (h) is given as 15 inches.
The area of each circular base is πr^2. Therefore, the area of both bases is 2πr^2.
The lateral area of the cylinder is given by the formula 2πrh.
Substituting the values we have:
Area of both bases = 2πr^2 = 2π(4.5)^2 = 2π(20.25) = 40.5π
Lateral area = 2πrh = 2π(4.5)(15) = 135π
Total surface area = area of both bases + lateral area = 40.5π + 135π = 175.5π
Approximating π to 3.14, we get:
Total surface area = 175.5π ≈ 175.5(3.14) ≈ 551.07
Therefore, the surface area of the cylinder is approximately 551.07 square inches.