Question : The following formula is used to calculate which of the following? $\frac{\text { Angle of arc at centre }}{360°} \times \pi \times \text{Diameter}$
Option 1: Length of a sector
Option 2: Area of an arc
Option 3: The radius of a circle
Option 4: Length of an arc
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Correct Answer: Length of an arc
Solution : The circumference of a circle = $2\pi r$ So, the length of an arc $=\frac{\text{Angle of arc at centre}(\theta)}{360°}×2\pi r$ $=\frac{\text { Angle of arc at centre }}{360°} \times \pi \times \text{diameter}$ Hence, the correct answer is 'Length of an arc'.
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Question : The area of the sector of a circle of radius 12 cm is $32 \pi \;\mathrm{cm}^2$. Find the length of the corresponding arc of the sector.
Question : Find the length of the arc of the sector of a circle of diameter 7 cm with a central angle of $108^{\circ}$. [Use $\pi=\frac{22}{7}$]
Question : The area of a sector of a circle is 110 cm2 and the central angle of the sector is 56°, what is the circle's radius? (Take $\pi=\frac{22}{7}$)
Question : The area of a sector is 1848$\mathrm{~m}^2$ and the central angle of the sector is $270°$. Find the radius of the circle. (Take $\pi=\frac{22}{ 7}$)
Question : The radius of a circle with centre at O is 6 cm and the central angle of a sector is 40°. Find the area of the sector.
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