First slide

Accuracy; precision of instruments and errors in measurements

Question

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

Moderate

A

$(51.4 \pm 26.4) {cm}^{2}$
B

$(55.4 \pm 26.4) {cm}^{2}$
C

$(65.4 \pm 26.4) {cm}^{2}$
D

$(23.4 \pm 26.4) {cm}^{2}$

Solution

$S = 4 π r^{2} = 4 π (2.1)^{2} = 55.4 {cm}^{2}$
$\frac{Δ S}{S} = 2 \times \frac{Δ r}{r}$
$Δ S = 2 \times \frac{Δ r}{r} \times S$
$= 2 \times \frac{0.5}{2.1} \times 55.4$
$= 26.4 {cm}^{2}$
$(S \pm Δ S) = (55.4 \pm 26.4) {cm}^{2}$

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