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 in2
1,306.90 in squared

2,613.81 in2
2,613.81 in squared

1,041.44 in2
1,041.44 in squared

816.81 in2

Answer 1

To calculate the surface area of a cylinder (which is the shape of a drum), you can use the formula:

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

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

Given that the diameter of Peter's drum is 13 inches, we can find the radius:

\[ r = \frac{\text{diameter}}{2} = \frac{13}{2} = 6.5 \text{ inches} \]

The height \( h \) of the drum is given as 19 inches.

Now, substitute the values into the surface area formula:

\[ \text{Surface Area} = 2\pi (6.5)(19 + 6.5) \]

Calculating \( h + r \):

\[ h + r = 19 + 6.5 = 25.5 \]

Now, calculate the surface area:

\[ \text{Surface Area} = 2\pi (6.5)(25.5) \]

Now, calculate \( 2 \times 6.5 = 13 \):

\[ \text{Surface Area} \approx 13\pi(25.5) \]

Calculating \( 13 \times 25.5 \):

\[ 13 \times 25.5 = 331.5 \]

Now, multiply by \( \pi \) (using \( \pi \approx 3.14 \)):

\[ \text{Surface Area} \approx 331.5 \times 3.14 \approx 1,041.44 \text{ in}^2 \]

The approximate surface area of Peter’s drum is:

1,041.44 in²

So the correct answer is:

1,041.44 in².