Final answer:
The cylindrical can with a 1000 cm³ water capacity and the least quantity of metal has a radius of about 7.76 cm.
Step-by-step explanation:
To find the radius of a cylindrical can containing 1000 cm³ of water using the minimum amount of metal, we rearranged the formula for the volume of a cylinder and substituted the values to calculate the radius.
To find the radius of a cylindrical can to contain 1000 cm³ of water using the minimum amount of metal, we need to calculate the radius using the given volume of water.
Using the formula for the volume of a cylinder, V = πr²h, we can rearrange the formula to solve for the radius:
r = √(V / (πh))
Substituting in the values, we get:
r = √(1000 cm³ / (3.142 × 5.25 cm))
r ≈ √(60.0962) ≈ 7.76 cm
Therefore, the radius of the cylindrical can that contains 1000 cm³ of water using the minimum amount of metal is approximately 7.76 cm.