A Machinist Is Required to Manufacture a Circular Metal Disk $1000 \mathrm {~cm} ^ { 2 }$

Multiple Choice

A machinist is required to manufacture a circular metal disk with area $1000 \mathrm {~cm} ^ { 2 }$ . If the machinist is allowed an error tolerance of $\pm 15 \mathrm {~cm} ^ { 2 }$ in the area of the disk, how close to the ideal radius must the machinist control the radius?
Round your answer to the nearest hundred thousandth. Select the correct answer.

A) $\delta \leq 0.13131 \mathrm {~cm}$
B) $\delta \leq 0.13281 \mathrm {~cm}$
C) $\delta \leq 0.13231 \mathrm {~cm}$
D) $\delta \leq 0.13331 \mathrm {~cm}$
E) $\delta \leq 0.13431 \mathrm {~cm}$