QuestionAugust 27, 2025

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 14 mm 15 mm 16 mm 17 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 14 mm 15 mm 16 mm 17 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 14 mm 15 mm 16 mm 17 mm

Solution
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Answer

16 mm Explanation 1. Calculate the area for each radius Use the formula for the area of a circle: **A = \pi r^2**. Calculate for each given radius. - For r = 14 mm: A = 3.14 \times 14^2 = 615.44 mm² - For r = 15 mm: A = 3.14 \times 15^2 = 706.5 mm² - For r = 16 mm: A = 3.14 \times 16^2 = 803.84 mm² - For r = 17 mm: A = 3.14 \times 17^2 = 907.46 mm² 2. Determine which areas fall within the range Check which calculated areas are between 800 and 900 mm². - 803.84 mm² (for r = 16 mm) is within the range.

Explanation

1. Calculate the area for each radius<br /> Use the formula for the area of a circle: **$A = \pi r^2$**. Calculate for each given radius.<br />- For $r = 14$ mm: $A = 3.14 \times 14^2 = 615.44$ mm²<br />- For $r = 15$ mm: $A = 3.14 \times 15^2 = 706.5$ mm²<br />- For $r = 16$ mm: $A = 3.14 \times 16^2 = 803.84$ mm²<br />- For $r = 17$ mm: $A = 3.14 \times 17^2 = 907.46$ mm²<br /><br />2. Determine which areas fall within the range<br /> Check which calculated areas are between 800 and 900 mm².<br />- $803.84$ mm² (for $r = 16$ mm) is within the range.
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