The surface area of a cylinder is given by the formula:
A = 2πr² + 2πrh
where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi, which is approximately equal to 3.14.
In this case, we are given that the cylinder has a diameter of 15 inches, so the radius is 7.5 inches (half of the diameter). We are also given that the height of the cylinder is 5 inches. Using these values in the formula, we can calculate the surface area of the cylinder as:
A = 2π(7.5)² + 2π(7.5)(5)
= 2π(56.25) + 2π(37.5)
= 2(π)(93.75)
= 187.5π
≈588.75
Therefore,
we need approximately 588.75 square inches of leather to create the travel case.