Question

The radius of a sphere is measured as (20.5+-0.5)cm. Calculate its surface area with error limits.

Answer 1

The surface area of a sphere is given by,

A = 4πr²,

where r is the radius of the sphere.

So, the measured value of area,

A = 4π (20.5)² = 5281.0 cm²

And, the relative error,

∆A / A = 2 · ∆r / r = 1 / 20.5

=> ∆A = 4π (20.5)² / 20.5 = 257.6 cm²

Hence the surface area is,

A = (5281.0 ± 257.6) cm²