Subjects geometry

Semicircle Diameter

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Semicircle Diameter


1. The problem describes a semicircle with a radius of 7.2 meters and a horizontal diameter of 7.2 meters. This indicates possibly a misunderstanding since the diameter should be twice the radius. 2. Recall the relationship between radius ($r$) and diameter ($d$): $$d = 2r$$ 3. Given the radius $r = 7.2$, compute the diameter: $$d = 2 \times 7.2 = 14.4$$ meters 4. So, the correct diameter of the semicircle should be 14.4 meters, not 7.2 meters. 5. The semicircle shape can be described by the function of a circle with radius 7.2 centered at the origin: $$x^2 + y^2 = 7.2^2 = 51.84$$ 6. Since it's a semicircle (upper half), solve for $y$: $$y = \sqrt{51.84 - x^2}$$ 7. The domain of $x$ is all real numbers between $-7.2$ and $7.2$ for this semicircle. 8. Summary: The semicircle with radius 7.2m has diameter 14.4m and equation $$y = \sqrt{51.84 - x^2}$$ over $-7.2 \leq x \leq 7.2$.