Answer: 7.35 inches
Explanation:
The formula for the surface area of a cylinder is 2πrh + 2πr^2, where r is the radius and h is the height of the cylinder.
Given that the diameter of the tub is 10 inches, the radius (r) is half of that, which is 5 inches.
So, the equation for the surface area of the cylinder can be written as:
2π(5)(h) + 2π(5)^2 = 387.79
Simplifying the equation gives:
10πh + 50π = 387.79
Dividing both sides by 10π gives:
h + 5 = 12.34
Subtracting 5 from both sides gives:
h = 7.34
Therefore, the height of the tub is 7.35 inches (rounded to two decimal places).