Subjects geometry

Circle Measurements

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Circle Measurements


1. The problem requires us to complete the table by finding missing diameters and areas of circles given some radius and diameter values. We use the formulas: - Diameter $d = 2r$ where $r$ is the radius. - Area $A = \pi r^2$ with $\pi = 3.14$. 2. Given radius 12 m (row 1): - Diameter $= 2 \times 12 = 24$ m. - Area $= 3.14 \times 12^2 = 3.14 \times 144 = 451.84$ m² (not asked but just for clarity). 3. For diameter 16 in (row 2): - Radius $r = \frac{16}{2} = 8$ in. - Area $= 3.14 \times 8^2 = 3.14 \times 64 = 200.96$ in². 4. For area $153.86$ cm² (row 4): - Use $A = 3.14 r^2$ to find radius: $$r^2 = \frac{153.86}{3.14} = 49$$ $$r = \sqrt{49} = 7 \text{ cm}$$ - Diameter $= 2 \times 7 = 14$ cm. 5. For diameter missing in row 3 with radius 12 m (already done): diameter is 24 m. 6. For area missing in row 5 with radius 12 m (already done step 2): area is $451.84$ m². Summary of missing values: - Row 1 diameter: 24 m - Row 2 area: 200.96 in² - Row 3 diameter: 24 m (same as row 1 radius) - Row 4 radius: 7 cm, diameter: 14 cm - Row 5 area: 451.84 m² Final answers: | Radius | Diameter | Area | |--------|----------|------------| | 12 m | 24 m | 451.84 m² | | 8 in | 16 in | 200.96 in² | | 7 cm | 14 cm | 153.86 cm² |