Diameter of the sphere is measured as 20.0 ± 0.1 mm. The surface area of the sphere is [take π = 3]

The formula for the surface area of a sphere is 4πr², where r is the radius of the sphere.

Step 1: Convert the diameter to radius. The radius is half of the diameter. So, r = 20.0 mm / 2 = 10.0 mm.

Step 2: Substitute the radius into the formula. The surface area A = 4 * 3 * (10.0 mm)² = 1200 mm².

The uncertainty in the diameter is ±0.1 mm, so the uncertainty in the radius is ±0.05 mm.

Step 3: Calculate the uncertainty in the surface area. The formula for the uncertainty in a calculated quantity is given by the sum of the relative uncertainties in the measured quantities.

The relative uncertainty in the radius is ±0.05 mm / 10.0 mm = ±0.005 or ±0.5%.

The relative uncertainty in the surface area is therefore 2 * 0.5% = 1.0%, because the radius is squared in the formula for the surface area.

Step 4: Calculate the uncertainty in the surface area. The uncertainty in the surface area is 1.0% of 1200 mm² = ±12 mm².

So, the surface area of the sphere is 1200 ± 12 mm².