Question

To keep Paul Senior from blowing a gasket, Paul Junior must deviate from the ideal area of the disk, which is 1100 in², by less than plus minus 4 in². How close to the ideal radius must the Flowjet (the machine that cuts the disk) be to maintain tranquility at OCC?

Answer 1

The ideal radius for the Flowjet to maintain the disk's area within plus or minus 4 in² of the ideal 1100 in² is calculated by solving the area formula for the circle. The maximum and minimum radii that maintain the disk's area within this tolerance are √(1104/π) and √(1096/π), respectively.

Step-by-step explanation:

To determine how close to the ideal radius of a disk the Flowjet must be to keep the deviation of the disk's area within plus or minus 4 in² of the ideal 1100 in², we first need to recall the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.

Let's calculate the maximum and minimum allowable radii that correspond to the maximum and minimum areas. To get the maximum area (1104 in²), we solve the equation πr^2 = 1104 for r. Simultaneously, we solve πr^2 = 1096 for the minimum area to get the minimum radius.

Now solving for r, we get the allowable radii range:

• Maximum radius, r_max = √(1104/π)
• Minimum radius, r_min = √(1096/π)

To maintain tranquility at OCC, the Flowjet must cut the disk with a radius within this range.