Question #157933

Length of an arc

Find the length of an arc of a circle having the radius of 8 cm and subtended by a central angle of 330°.

Find the radius of a circle subtended by a central angle of π/4 radius and having an arc length of π.

On a circle of radius 100 cm, the arc intercepted a central angle of 3π/4. What is the arc length?

Expert's answer

**a. **length of an arc = 2"\\pi r(\\frac{{1}}{360}\\theta)"

"l=" "2 \\times \\pi \\times 8 \\times (\\frac{{330}}{360}) = 46. 0767"

"l" = 46.0767 cm

**b.**

"\\theta" = "\\frac{1}{4}\\pi" = 45"^0"

"l=" "2 \\times \\pi \\times r \\times (\\frac{{45}}{360})"

but "l=\\pi"

then

"\\pi=" "2 \\times \\pi \\times r \\times (\\frac{{45}}{360})"

"r= \\frac{360}{45 \\times2}= 4"

**c.**

"l=" "2 \\times \\pi \\times 100\\times (\\frac{{135}}{360}" )

"l=" 75"\\pi"

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