To find the surface area of a cylindrical drum, we can use the formula for the surface area (SA) of a cylinder, which is:
\[ SA = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given that the diameter of the drum is 13 inches, we can find the radius:
\[ r = \frac{diameter}{2} = \frac{13}{2} = 6.5 \text{ inches} \]
The height \( h \) is given as 19 inches.
Now we can substitute these values into the surface area formula:
\[ SA = 2\pi(6.5)(19 + 6.5) \]
Calculating \( h + r \):
\[ h + r = 19 + 6.5 = 25.5 \text{ inches} \]
Now substituting back into the formula:
\[ SA = 2\pi(6.5)(25.5) \]
Calculating \( 2 \times 6.5 \):
\[ 2 \times 6.5 = 13 \]
Now we need to calculate:
\[ SA = 13\pi(25.5) \]
Using \( \pi \approx 3.14 \):
\[ SA \approx 13 \times 3.14 \times 25.5 \]
Calculating \( 13 \times 3.14 \):
\[ 13 \times 3.14 \approx 40.82 \]
Now multiply \( 40.82 \times 25.5 \):
\[ SA \approx 40.82 \times 25.5 \approx 1041.91 \text{ in}^2 \]
So, rounding to two decimal places, the approximate surface area of Peter’s drum is:
\[ \approx 1,041.44 \text{ in}^2 \]
Thus, the answer is:
1,041.44 in.²
This matches the response option: 1,041.44 in².