Final answer:
The volume of a cylindrical soda can is found by the formula V = πr²h. Given the volume and radius, the height can be found by rearranging the formula to h = V / (πr²), yielding a height of approximately 12 cm.
Step-by-step explanation:
The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder. In this question, we are given the volume V = 404.6 cm³ and the radius r = 3.25 cm, and we are asked to solve for the height h. We can do this by rearranging the formula to get h = V / (πr²).
Substituting in the given values gives h = 404.6 cm³ / (π * (3.25 cm)²). Calculating this gives h ≈ 12 cm. So, the height of the soda can is approximately 12 cm.
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