The formula for the surface area of a cylinder is:
Surface Area = 2πr^2 + 2πrh
where r is the radius of the base of the cylinder, h is the height, and π (pi) is a mathematical constant approximately equal to 3.14159.
We know that the surface area of the cylinder is 100.48 square centimeters. We can also assume that the radius of the cylinder is the same for both circular faces.
So we have:
100.48 = 2πr^2 + 2πrh
We can simplify this equation by factoring out 2πr:
100.48 = 2πr(r + h)
Now we can solve for h by isolating the variable on one side of the equation:
100.48 = 2πr(r + h)
Divide both sides by 2πr:
50.24/r = r + h
Subtract r from both sides:
h = 50.24/r - r
We still need the value of the radius to solve for the height. Without that information, we cannot calculate the height.