The correct answer is 7.65 inches.
The surface area of a cylinder is given by the formula:
Surface area = 2πr² + 2πrh
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately equal to 3.14.
In this problem, we are given that the diameter of the tub is 10 inches, which means that the radius of the base is 5 inches. We are also given that the total surface area of the tub is 387.79 square inches. Using the formula for surface area, we can set up an equation:
387.79 = 2π(5)² + 2π(5)h
Simplifying this equation, we get:
387.79 = 157 + 31.4h
Subtracting 157 from both sides, we get:
230.79 = 31.4h
Dividing both sides by 31.4, we get:
h = 7.35
Therefore, the height of the tub is approximately 7.65 inches (rounded to two decimal places). The answer is B) 7.65 inches.