Q. If the radius of a sphere is measured to be $\left(\right.2.1\pm0.05\left.\right)cm.$ Calculate the surface area (in $cm^{2}$ ) .

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A

$54.45\pm2.46$

B

$55.44\pm2.64$

C

$52.03\pm4.26$

D

$45.54\pm2.68$

Solution:

$S=4\left(\pi r\right)^{2}=4\times \frac{22}{7}\times \left(\right.2.1\left(\left.\right)^{2}$
$=55.44cm^{2}$
$\frac{\Delta S}{S}=2\left(\frac{\Delta r}{r}\right)$
$ΔS=2\left(\frac{Δr}{r}\right)S$
$=\frac{2 \times 0 . 05 \times 55 . 44}{2 . 1}=2.64$
$\therefore ΔS=\left(\right.55.44\pm2.64\left.\right)\left(cm\right)^{2}$

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