The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere.
Given that the surface area is 64π sq. in., we can equate the formula to the given surface area:
4πr^2 = 64π
Solving for r:
r^2 = 64π / 4π
r^2 = 16
r = √16
r = 4 inches
The ideal radius of the sphere should be 4 inches.
Now, to find the error tolerance, we can calculate the change in radius to achieve an error of ±2 sq. in. in the surface area.
The new surface area would be 64π + 2 and 64π - 2.
denote the ideal radius as r and the change in radius as δr.
For a change of +2 sq. in:
4π(r + δr)^2 = 64π + 2
For a change of -2 sq. in:
4π(r - δr)^2 = 64π - 2
Solving for δr in both cases will give us the required change in radius to achieve the specified error tolerance.
