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s=18cm,theta=54^(@); find r

s=18 cm,θ=54∘; \mathrm{s}=18 \mathrm{~cm}, \theta=54^{\circ} ; find r \mathrm{r}

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Q. s=18 cm,θ=54∘; \mathrm{s}=18 \mathrm{~cm}, \theta=54^{\circ} ; find r \mathrm{r}
  1. Convert to Radians: To find the radius rr, we can use the formula for the arc length of a circle, which is s=r×θs = r \times \theta, where θ\theta is in radians. First, we need to convert θ\theta from degrees to radians.\newlineθ\theta in radians = (54 degrees)×(π/180 degrees)=54π180=3π10(54 \text{ degrees}) \times (\pi/180 \text{ degrees}) = \frac{54\pi}{180} = \frac{3\pi}{10}
  2. Plug into Formula: Now plug the values into the arc length formula s=r⋅θs = r \cdot \theta.18 cm=r⋅(3π10)18 \, \text{cm} = r \cdot \left(\frac{3\pi}{10}\right)
  3. Solve for r: Solve for r by dividing both sides by (3π/10)(3\pi/10).\newliner=(18 cm)/(3π/10)=(18×10)/(3π)=60/(3π)r = (18 \, \text{cm}) / (3\pi/10) = (18 \times 10) / (3\pi) = 60 / (3\pi)
  4. Simplify Fraction: Simplify the fraction to find rr.r=20πr = \frac{20}{\pi} cm

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