A sector with an area of \goldE{26\pi\,\text{cm}^2}26πcm 2 start color #a75a05, 26, pi, start text, c, m, end text, squared, end color #a75a05 has a radius of \maroonD{6\,\text{cm}}6cmstart color #ca337c, 6, start text, c, m, end text, end color #ca337c. What is the central angle measure of the sector in radians?

13π/9 rad

Step-by-step explanation:

Given the following

Area of a sector = 26πcm²

radius of the sector = 6cm

Required

central angle measure of the sector in radians

Area of a sector = Ф/2π * πr²

26π = Ф/2π * πr²

26 = Ф(6)²/2π

26 = 36Ф/2π

2π = 36Ф/26

π = 18Ф/26

26π = 18Ф

Ф = 26π/18

Ф = 13π/9 rad

Hence the measure of the central angle in radians is  13π/9 rad

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step-by-step explanation:

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