A machinist is required to manufacture a circular metal disk with area 1100 cm2. (Round your answers to four decimal places.)

Question

A machinist is required to manufacture a circular metal disk with area 1100 cm^2. (Round your answers to four decimal places.)

 

(a) What radius produces such a disk?

(b) If the machinist is allowed an error tolerance of ±7 cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?

Answer 1

Part a)

 

Area of a circle is

 

A = πr²

 

 

r = √(1100 cm² / π)

 

r = 18.7121 cm

 

This is the outer radius of the disk.

 

 

Part b)

 

The maximum error in area = 1100 cm² + 7 cm²

                                         = 1107 cm²

 

The minimum error in area = 1100 cm² - 7 cm²

                                        = 1093 cm²

 

 

Maximum radius error = √(1107 cm²  / π)

                                = 18.7715 cm

 

Minimum radius error = √(1093 cm² / π)

                                = 18.6524 cm

 

 

The increment between the ideal radius and maximum radius is the same as the increment between the ideal radius and the minimum radius.

 

Find the increment to get how close the machinist needs to control the radius.