Question

A circle has a radius of 6 yards. A sector of the circle that is 12.56 yards² is painted. What is the angle measurement of the painted sector?

Answer 1

Given

• Circle's Radius = 6 yards
• Sector Area of Circle = 12.56 yards²

Explanation

As we know that we can find the angle subtended by the sector using formula as:-

$\bullet \ {\pink{\underline{\underline{\boxed{\sf{ Area_{(Sector)} = \dfrac{ \theta }{360^{ \circ } } \times πr^2 }}}}}} \\ \\ \\ \colon\implies{\sf{ 12.56 = \dfrac{ \theta }{360 } \times \dfrac{22}{7} \times (6)^2 }} \\ \\ \\ \colon\implies{\sf{ 12.56 = \dfrac{ \theta }{ \cancel{360} } \times \dfrac{22}{7} \times \cancel{36} }} \\ \\ \\ \colon\implies{\sf{ 12.56 = \dfrac{ \theta }{ 10 } \times \dfrac{22}{7} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{125.6 \times 7}{22} = \theta }} \\ \\ \\ \colon\implies{\sf{ \cancel{ \dfrac{879.2}{22} } = \theta }} \\ \\ \\ \colon\implies{\underline{\boxed{\sf\red{ \theta = 39.9 ^{ \circ } \ \ \ (40 ^{ \circ } ) }}}}$

Hence,

The angle measurement of the painted sector is 40° approximately.