Final answer:
To find the cylinder's height, the volume formula V = πr²h is rearranged to solve for height using the given radius and volume. Calculating the base area and dividing the volume by this figure, the height is determined to be approximately 4 feet.
Step-by-step explanation:
To find the height of a cylinder when given the volume of the cylinder and the radius, we use the formula V = πr²h. The volume (V) is provided as 1810 cubic feet, and the radius (r) is 12 feet. Plugging these values into the formula, we arrange to solve for the height (h).
Step 1: Write down the formula for the volume of a cylinder: V = πr²h.
Step 2: Substitute the given values into the formula: 1810 = π × 12² × h.
Step 3: Calculate the area of the base (πr²): π × 12² = 3.1416 × 144 ≈ 452.389 square feet.
Step 4: Divide the volume by the area of the base to find the height: h = 1810 ÷ 452.389 ≈ 4 feet.
Therefore, the height of the cylinder is approximately 4 feet.