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)

Question

Responses

816.81 in.2
816.81 in. squared

1,041.44 in.2
1,041.44 in. squared

2,613.81 in.2
2,613.81 in. squared

1,306.90 in.2

Answer 1

To find the surface area of a cylindrical drum, you can use the formula:

\[ \text{Surface Area} = 2\pi r(h + r) \]

where \( r \) is the radius and \( h \) is the height of the cylinder.

Given:

• Diameter = 13 inches, so the radius \( r = \frac{13}{2} = 6.5 \) inches.
• Height \( h = 19 \) inches.

Now, we can substitute these values into the formula:

\[ \text{Surface Area} = 2\pi (6.5)(19 + 6.5) \] \[ = 2\pi (6.5)(25.5) \] \[ = 2\pi (165.75) \] \[ \approx 2 \times 3.14159 \times 165.75 \] \[ \approx 1041.44 \text{ in}^2 \]

Thus, the approximate surface area of Peter's drum is 1,041.44 in².

The correct response from the options given is:

1,041.44 in.²