the circular face of a watch has an area that measures between 800 and 900 square millimeters. what could be…

the circular face of a watch has an area that measures between 800 and 900 square millimeters. what could be the radius of the watch face? use 3.14 for $pi$.\n14 mm\n15 mm\n16 mm\n17 mm

the circular face of a watch has an area that measures between 800 and 900 square millimeters. what could be the radius of the watch face? use 3.14 for $pi$.\n14 mm\n15 mm\n16 mm\n17 mm

Answer

Answer:

B. 15 mm

Explanation:

Step1: Recall area formula for circle

$A = \pi r^{2}$

Step2: Find lower - bound radius

$800=\pi r^{2}$, substituting $\pi = 3.14$, we get $r^{2}=\frac{800}{3.14}\approx254.78$, then $r=\sqrt{254.78}\approx15.96$ mm.

Step3: Find upper - bound radius

$900=\pi r^{2}$, substituting $\pi = 3.14$, we get $r^{2}=\frac{900}{3.14}\approx286.62$, then $r=\sqrt{286.62}\approx16.93$ mm. The radius should be between approximately 15.96 mm and 16.93 mm. So 16 mm is not in the range and 14 mm is too small. 17 mm is too large. The closest value among the options is 15 mm.