Answer to Question #100207 in Calculus for Max

Question

The ball circumference was measured and the result was p = 38.77 ± 0.20cm. By what accuracy can the ball surface be calculated?

Answer 1

The ball circumference is: $p = 38.77 \space \text{cm}$

The error of measurements is: $\Delta p = 0.2 \space \text{cm}$

The surface can be calculated by the formula: $S = \frac{1}{4\pi}p^2$

Taking the differential and keeping only linear part, find the error of surface calculations:

$\Delta S = \frac{1}{2\pi}p\cdot\Delta p$

Pluging numerical values obtain :

$\Delta S = 1.2 \space \text{cm}^2$

So, the surface can be measured with accuracy: $\pm1.2 \space \text{cm}^2$