Question

the radius of a circular plate is measured as 12.65cm instead of the actual length 12.5cm.find the absolute error in calculating the area of the circular plate

Answer 1

Answer:

Absolute error in calculating area = 2.41%

Step-by-step explanation:

Radius of plate = 12.65 cm

Area of Circular plate

$A_E=\pi\:r^2\\\\=\pi(12.65)^2\\\\=\pi\:160.0225 cm^2$

Radius of plate = 12.5 cm

Area of Circular plate

$A_C=\pi\:r^2\\\\=\pi \:(12.5)^2\\\\=\pi\:156.25 cm^2$

Error in measurement

$Error=A_E-A_C\\\\=\pi(160.0225-156.25)\\\\=\pi(3.7725)\\\\=11.86 cm^2$

Percentage error in measurement

$= \frac{Error}{A_C}\times100\\\\=\frac{\pi\times3.7725}{\pi\times156.25}\times100\\\\=2.41$

Hope it helps you.