Question

a machinist is required to manufacture a circular metal disk with area 600 cm². (a) what radius produces such a disk? (round your answer to four decimal places.) 13.8197 × cm

Explanation:

Step1: Recall area formula for circle

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius.

Step2: Solve for radius

Given $A = 600\ cm^{2}$, we have $600=\pi r^{2}$. Then $r^{2}=\frac{600}{\pi}$, and $r=\sqrt{\frac{600}{\pi}}$.

Step3: Calculate value of radius

$r=\sqrt{\frac{600}{\pi}}\approx\sqrt{\frac{600}{3.14159}}\approx\sqrt{190.9859}\approx 13.819765\approx13.8198$ (rounded to four - decimal places).

Answer:

$13.8198$ cm