A sphere's circumference was measured to be 88 cm w/ a possible error of 0.5 cm. Estimate the max error in the calculated surface area. Then, estimate the relative error in the calculated SA.

Question

Question is based on the Calculus principles of Linear Approximations & Differentials

Answer 1

Given: Circumference of the sphere is 88 cm with a possible error of ±0.5 cm.

1. The radius of the sphere is approximately 14.01 cm.

2. The error in the radius (dr) due to the measurement error in circumference is approximately 0.08 cm.

3. The maximum error in the calculated surface area of the sphere (dA) is approximately 28.01 cm².

4. The relative error in the calculated surface area is about 1.14%. This represents the proportion of the error in the surface area relative to the total calculated surface area.