Question

The measured radius of a circle is 80 m with a possible error of 0.05 m in its diameter. The error in the computed area will nearly be
1. + 6.5 m²
2. – 0.65 m²
3. ± 12.6 m²
4. ± 8.2 m²

Answer 1

Correct Answer - Option 3 : ± 12.6 m²

Given: Diameter =  160 m

Error in diameter, e_d = ± 0.05 m

Initial Area, \({A_i} = \frac{\pi }{4}{d^2} = \frac{\pi }{4} \times {\left( {160} \right)^2} = \) 20106.19 m³

Find area, \({A_g} = \frac{\pi }{4}{\left( {d \pm {e_d}} \right)^2} = \frac{\pi }{4}{\left( {160 \pm 0.05} \right)^2}\)

= 20118.76 m² (+ve sign)

= 20093.62 m² (-ve Sign)

Error in Area = Initial value – Find value

= 20106.19 – 20093.62

= + 12.56 m²