Question

True or False: A sector of a circle with a measure of 36° and radius of 12 cm has an arc length of about 7.5 cm.

Answer 1

True

Explanation:

The formula for an arc length when given a degree is:

`\displaystyle{\text{arclength} = 2\pi r \left( (\theta)/(360^(\circ)) \right)}`

Given radius (r) = 12 cm and measure (θ) = 36 degrees. Therefore:

`\displaystyle{\text{arclength} = 2\pi \left(12\right) \left( (36^(\circ))/(360^(\circ)) \right)}\\\\\displaystyle{\text{arclength} = 24\pi \cdot (1)/(10)}\\\\\displaystyle{\text{arclength} = (24\pi)/(10)}\\\\\displaystyle{\text{arclength} \approx 7.5 \ \: \text{cm}}`

Therefore, the statement is true.