A class is finding the radii of 3 cylinders. Cylinder A has a surface area of 4,163.64 in.2 .
Cylinder B has a surface area of 4,521.60 in.2 . Cylinder C has a surface area of 3,165.12 in.2 .
If the height of each cylinder is 22 inches, find the radius of each cylinder. Use 3.14 for π .
To find the radius of each cylinder, we first need to use the formula for the surface area of a cylinder:
Surface area = 2πrh + 2πr^2
Given the surface area and height of each cylinder, we can plug in the values and solve for the radius.
For Cylinder A:
4,163.64 = 2(3.14)r(22) + 2(3.14)r^2
4,163.64 = 138.16r + 6.28r^2
6.28r^2 + 138.16r - 4,163.64 = 0
Solving this quadratic equation, we find that r ≈ 17.67 inches for Cylinder A.
For Cylinder B:
4,521.60 = 2(3.14)r(22) + 2(3.14)r^2
4,521.60 = 138.16r + 6.28r^2
6.28r^2 + 138.16r - 4,521.60 = 0
Solving this quadratic equation, we find that r ≈ 18.1 inches for Cylinder B.
For Cylinder C:
3,165.12 = 2(3.14)r(22) + 2(3.14)r^2
3,165.12 = 138.16r + 6.28r^2
6.28r^2 + 138.16r - 3,165.12 = 0
Solving this quadratic equation, we find that r ≈ 14.51 inches for Cylinder C.
Therefore, the radius of Cylinder A is approximately 17.67 inches, the radius of Cylinder B is approximately 18.1 inches, and the radius of Cylinder C is approximately 14.51 inches.