Final answer:
To find the volume of a cylinder with a given base area and height, calculate the radius by taking the square root of the base area divided by π. Then, find the height by adding 4 to the radius. Finally, plug the values of the radius and height into the formula V = πr²h to find the volume.
Step-by-step explanation:
To find the volume of a cylinder, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. Given that the base of the cylinder has an area of 169π cm², we can determine the radius by taking the square root of the area divided by π. Once we have the radius, we can find the height by adding 4 cm to the radius. Finally, we can substitute the values of the radius and height into the formula to find the volume.
In this case, the radius = √(169π/π) = 13 cm. The height = radius + 4 cm = 13 cm + 4 cm = 17 cm. Thus, the volume V = π(13 cm)²(17 cm) ≈ 9079.3 cm³. Rounded to the nearest tenth, the volume of the cylinder is approximately 9079.3 cm³.