Final answer:
To find the total surface area of the remaining portion, calculate the surface area of the sphere, subtract the surface area of the caps, resulting in 0 in².
Step-by-step explanation:
To determine the total surface area of the remaining portion of a wooden sphere after two equal caps have been removed, we need to calculate the surface area of the sphere and subtract the surface area of the caps.
First, let's find the surface area of the sphere using the formula: Surface area = 4πr², where r is the radius of the sphere.
Given that the diameter of the sphere is 11.8 in, the radius is half of the diameter, so r = 11.8 in / 2 = 5.9 in.
Substituting the value of r in the formula, we have: Surface area = 4π(5.9 in)² = 4π(34.81 in²) = 138.52π in².
Next, let's find the surface area of the two caps that have been removed. Since the caps are equal, each cap will have a surface area of half the surface area of a full sphere.
Therefore, the surface area of one cap is: Surface area of one cap = 138.52π in² / 2 = 69.26π in².
Finally, to find the total surface area of the remaining portion, we subtract the surface area of the two caps from the surface area of the whole sphere:
Total surface area of remaining portion = Surface area of sphere - 2 × Surface area of cap = 138.52π in² - 2 × (69.26π in²) = 138.52π in² - 138.52π in² = 0 in².