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?(1 point)
Responses
1,041.44 in.2
1,041.44 in. squared
816.81 in.2
816.81 in. squared
1,306.90 in.2
1,306.90 in. squared
2,613.81 in.2
The surface area of a cylinder can be calculated using the formula 2πr^2 + 2πrh, where r is the radius and h is the height.
Given that the diameter is 13 inches, the radius would be half of that, which is 6.5 inches. The height is 19 inches.
Surface area = 2π(6.5)^2 + 2π(6.5)(19)
Surface area = 2π(42.25) + 2π(123.5)
Surface area = 84.5π + 247π
Surface area = 331.5π
Approximating π to 3.14159, we get:
Surface area ≈ 331.5 * 3.14159
Surface area ≈ 1041.44 in^2
Therefore, the approximate surface area of Peter's drum is 1,041.44 in^2, which is closest to the first option.