Final answer:
The height of the cylinder is calculated by rearranging the volume formula to solve for h, yielding the formula h = V / (πr²). For a cylinder with a volume of 367 cm³ and a radius of 3 cm, the height is approximately 12.98 cm.
Step-by-step explanation:
To find the formula for height h in terms of the cylinder's volume V, the radius r, and Pi (π), we rearrange the volume formula V = πr²h to solve for h by dividing both sides by πr².
h = V / (πr²)
Using this rearranged formula, we can calculate the height of a cylinder with a volume of 367 cm³ and a radius of the base of 3 cm. First, we plug the values into the formula:
h = 367 / (π × 3²)
Perform the calculation:
h = 367 / (π × 9)
h = 367 / 28.274
h ≈ 12.98 cm
The height of a cylinder with a volume of 367 cm³ and a radius of 3 cm is approximately 12.98 cm.