Answer :
The radius of the container is then r = 1 in. and the height is h = 12.15 in.
The volume of a right circular cylinder is given by the formula V = πr^2h, where r is the radius, h is the height, and π is a constant approximately equal to 3.14. We are given that V = 38 in.3, so we can write the equation 38 = πr²h. To minimize the amount of metal used, we want to minimize either the radius or the height (since the volume is fixed). Since h is squared in the formula, it is more effective to minimize the radius.
If we let r = 1, then the equation becomes 38 = π(1)²h, or 38 = πh. Solving for h, we get h = 38/π ≈ 12.15.
Thus, the radius of the container is then r = 1 in. and the height is h = 12.15 in.
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