Question

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 π. 15 mm 17 mm 16 mm 14 mm

Explanation:

Step1: Recall the formula for the area of a circle

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

Step2: Calculate the area for each radius option

• For \(r = 14\) mm:

\(A=\pi r^{2}=3.14\times14^{2}=3.14\times196 = 615.44\) mm²

• For \(r = 15\) mm:

\(A=\pi r^{2}=3.14\times15^{2}=3.14\times225 = 706.5\) mm²

• For \(r = 16\) mm:

\(A=\pi r^{2}=3.14\times16^{2}=3.14\times256 = 803.84\) mm²

• For \(r = 17\) mm:

\(A=\pi r^{2}=3.14\times17^{2}=3.14\times289 = 907.46\) mm²

Answer:

\(16\) mm