Final answer:
The height of a cylinder with a volume of 1 and 2/9 in³ and a radius of 1/3 in, using π approximated as 22/7, is approximately 7/3 inches or about 2.333 inches.
Step-by-step explanation:
To determine the height of a cylinder with a given volume, we use the formula for the volume of a cylinder, which is V = πr²h, where V is volume, r is radius, and h is height. In this case, the volume (V) is 1 and 2/9 in³ (which is approximately 1.222 in³) and the radius (r) is 1/3 in. Approximating π as 22/7, we can solve for the height (h) using the following steps:
First, convert the mixed number for volume to an improper fraction: 1 and 2/9 = 11/9 in³.
Next, plug the numbers into the volume formula: (22/7) × (1/3 in)² × h = 11/9 in³.
Simplify and solve for h: (22/7) × (1/9 in²) × h = 11/9 in³.
Multiply both sides by (7/22) × (9 in²) to isolate h: h = (11/9 in³) × (7/22) × (9 in²).
The 9's and the 22 cancel out, leaving h = 7/3 in.
Therefore, the height of the cylinder is approximately 7/3 inches or about 2.333 inches.