Final answer:
The height of a cylinder with a volume of 1526.04 cubic inches and a diameter of 18 inches is approximately 6 inches, calculated using the volume formula for a cylinder (V = πr²h) and solving for the height.
Step-by-step explanation:
To find the height of a cylinder with a volume of 1526.04 in³ and a diameter of 18 inches, we use the volume formula for a cylinder, V = πr²h. First, we must calculate the radius of the cylinder, which is half the diameter. So, the radius (r) is 18 in / 2 = 9 in. Next, we can rearrange the formula to solve for the height (h):
h = V / (πr²)
Substituting the given values and using 3.14 as an approximation for π, we have:
h = 1526.04 in³ / (3.14 × (9 in)²)
h = 1526.04 in³ / (3.14 × 81 in²)
h = 1526.04 in³ / 254.34 in²
h ≈ 6 in
Therefore, the height of the cylinder is approximately 6 inches.