Peter plays renaissance drums, Which are cylindrical in shape, in military reenactments in his hometown. He just bought a new drum with the money he has saved from working. Peter's new drum has a diameter of 13 inches and a height of 19 inches. what is the approximate surface area of peter's drum?
A. 1,306.90 in^2
B. 2,613.81 in^2
C. 816.81 in^2
D. 1,041.44 in^2
To find the surface area of Peter's drum, we need to calculate the surface area of the two circular ends and the lateral surface area:
1. The surface area of each circular end can be calculated using the formula for the area of a circle: A = πr^2, where r is the radius (half the diameter) of the end.
Area of one end = π(13/2)^2 = π(6.5)^2 = 42.25π in^2
Area of both ends = 2 * 42.25π in^2 = 84.5π in^2
2. The lateral surface area of a cylinder can be calculated using the formula: A = 2πrh, where r is the radius of the cylinder and h is the height.
Lateral surface area = 2π(13/2)(19) = 2π(6.5)(19) = 247π in^2
3. Total surface area = Area of both ends + Lateral surface area
Total surface area ≈ 84.5π + 247π = 331.5π ≈ 1041.44 in^2
Therefore, the approximate surface area of Peter's drum is 1,041.44 in^2, which is option D.