Find the radius of the cylinder

Given the internal diameter is $78\text{ m}$, the radius $r$ is half of the diameter.

$r = \frac{78}{2} = 39\text{ m}$

Set up the formula for an open cylinder

Since the drum is open at the top, the inner surface area includes the curved surface area and the area of the circular base.

$A = 2\pi r h + \pi r^2$

Substitute the values

Substitute $r = 39\text{ m}$ and $h = 79\text{ m}$ into the surface area equation.

$A = 2 \times \pi \times 39 \times 79 + \pi \times 39^2$

Calculate the final area

Compute the numerical values: $2 \times \pi \times 39 \times 79 \approx 19,361.95$ and $\pi \times 39^2 \approx 4,778.36$, leading to the total inner surface area.

$A \approx 28,926.9\text{ m}^2$