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

1,306.90 in.2
1,306.90 in. squared

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

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 of the cylinder,
• \( h \) is the height of the cylinder,
• \( \pi \) is approximately 3.14.

Given:

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

Now we can calculate the surface area:

1. Calculate the term \( h + r \): \[ h + r = 19 + 6.5 = 25.5 \text{ inches} \]

2. Now, plug in the values into the surface area formula: \[ \text{Surface Area} = 2 \pi (6.5)(25.5) \]

3. Calculate \( 2 \pi (6.5)(25.5) \): \[ \approx 2 \times 3.14 \times 6.5 \times 25.5 \]

4. First, calculate \( 6.5 \times 25.5 \): \[ 6.5 \times 25.5 \approx 165.75 \]

5. Then calculate \( 2 \pi (165.75) \): \[ 2 \times 3.14 \times 165.75 \approx 6.28 \times 165.75 \approx 1041.44 \]

So the approximate surface area of Peter’s drum is:

\[ \text{Surface Area} \approx 1,041.44 \text{ in.}^2 \]

Thus, the correct response is:

1,041.44 in.².