Final answer:
The diameter of the cylinder is calculated using the formula for the volume of a cylinder, with the given volume and height. The radius is obtained first, and then the diameter is found by doubling the radius.
Step-by-step explanation:
To find the diameter of the cylinder, we'll use the volume formula for a cylinder: V = πr²h, where V is volume, r is radius, and h is height. Given that the volume (V) of the cylinder is 2,908.33 in³ and the height (h) is 7 inches, we can rearrange the formula to solve for the radius (r): r² = V / (πh). Plugging the values into this equation, we get: r2 = 2,908.33 / (π × 7). Once we calculate the radius, to find the diameter, we simply multiply the radius by 2.
From the given options, we identify the correct diameter in the form of n inches. To find the diameter of the cylinder, we can rearrange the formula for the volume of a cylinder: V = πr²h. Substituting the given values, we have: 2908.33 = 3.142 × r² × 7. Simplifying the equation: 2908.33 = 21.994 × r2. Dividing both sides by 21.994: r² = 132.21. Taking the square root of both sides: r = 11.50. Therefore, the diameter of the cylinder is twice the radius, which is 2 × 11.50 = 23 inches.