Problem 11b

Given information

The area of the circular metal disk is .

The tolerance in the area of the disk is .

Step-by-step explanation

• The tolerance in the area of the disk is .
• Write the inequality by using the fact that tolerance in the area of the disk is and the area of the disk is .
• Consider as radius and as . The area is given by . Therefore . That implies .
• It can be observed that .
• Substitute for in the equation (1).
• Solve the inequality in the equation (2) by using the fact that if  then .
• It is required to be find that how close to the ideal radius in part (a) must the machinist control the radius. That is we have to find the tolerance in the radius.
• Let the tolerance in the radius as .
• Write the inequality involving the fact that the tolerance of the radius is .