Question

A machinist is required to manufacture a circular metal disk with area 500 cm2.. (a) What radius produces such a disk? (Round your answer to four decimal places.). . . cm. . (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? (Round your answers to four decimal places.). cm

Answer 1

We are given with an area of a disk equal to 500 cm2. Area of a circle is equal to pi r^2. Hence the radius of the disk is equal to (500/pi)^0.5 or equal to 12.6159 cm. If the area is equal to 507 cm^2, then r is equal to 12.7039 cm, while if the area is 493 cm2, the radius is 12.5272 cm. The percent difference is 0.7% and 0.69%