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

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

(b)
`(dA)/(A)=(32.66)/(4245.28)=0.0077`

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 * 3.14* 26* 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

`(dA)/(A)=(32.66)/(4245.28)=0.0077`

Answer 2

(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%.

Explanation:

Here the given are,

The Radius of the circle r = 26cm.

The maximum error in measurement dr = 0.2 cm.