Question

The radius of a sphere in measured to be $(2.1\pm 0.5)$cm. Calculate its surface area with error limits.

Answer 1

surface area of sphere

$A=4\pi r^2$

$a=4\times 3.14\times {\left(2.1\right)}^2$

$=55.4{cm}^2$

$A=4\pi r^2$

$A=4\times 3.14\times {\left(2.1\right)}^2$

$=55.4{cm}^2$\\ $\frac{\Delta A}{A}=2\times \frac{\Delta r}{r}$

$\Delta A=2\times \frac{\Delta r}{r}\times A$

$=2\times \frac{0.5}{2.1}\times 55.4$

$=26.4{cm}^2$

Surface area =$(55.4\pm 26.4)c{m}^2$