Question

if error is measurement of a radius of a sphere 1% .what will be the error in measurement of volume .​

Answer 1

Volume = 4πR³/3

ΔV/V × 100 = 3(∆R / R) × 100

= 3 × (1/100) × 100

= 3

∴ Percentage error in volume is 3%

Answer 2

Solution:-

Given:-

$\mathtt{\frac{\triangle r}{r}\times 100 = 1\%}$

$\mathtt{We\;know\;that,\;V=\frac{3}{4}\pi r^{3}}$

$\mathtt{Then,}$

$\mathtt{\frac{\triangle V}{V}\times 100 = \pm3 \big(\frac{\triangle r}{r}\times 100 \big) = \pm3 \times 1 = \pm 3\%}$