Question

The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error

Answer 1

Answer:

(a) Hence the maximum error in the calculated area of the disk is 32.67$cm^{2}$.

(b) Hence the relative error is 1.54%.

Step-by-step explanation:

Here the given are,

The Radius of the circle r = 26cm.

The maximum error in measurement dr = 0.2 cm.

Answer 2

Answer:

(a) $A =(4245.28\pm32.66) cm^2$

(b) $\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077$

Step-by-step explanation:

radius, r = 26 cm

error = 0.2 cm

(a) The area of the disc is given by

$A = \pi r^2\\\\dA = 2\pi r dr\\\\dA = 2 \times 3.14\times 26\times 0.2= 32.66$

Now

A = 3.14 x r x r = 3.14 x 26 x 26 = 4245.28 cm^2

So, the area with error is given by

$A =(4245.28\pm32.66) cm^2$

(b) The relative error is

$\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077$