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. 14 mm 15 mm 16 mm 17 mm

Explanation:

Step1: Recall the area formula for a circle

The area \( A \) of a circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius and \( \pi \) is approximated as 3.14.

Step2: Calculate the area for each radius option

• For \( r = 14 \) mm:

\( A = 3.14 \times 14^2 = 3.14 \times 196 = 615.44 \) square millimeters. (This is less than 800, so not valid.)

• For \( r = 15 \) mm:

\( A = 3.14 \times 15^2 = 3.14 \times 225 = 706.5 \) square millimeters. (This is less than 800, so not valid.)

• For \( r = 16 \) mm:

\( A = 3.14 \times 16^2 = 3.14 \times 256 = 803.84 \) square millimeters. (This is between 800 and 900.)

• For \( r = 17 \) mm:

\( A = 3.14 \times 17^2 = 3.14 \times 289 = 907.46 \) square millimeters. (This is greater than 900, so not valid.)

Answer:

16 mm (or the option corresponding to 16 mm, e.g., if the options are labeled as A. 14 mm, B. 15 mm, C. 16 mm, D. 17 mm, then the answer is C. 16 mm)