Respuesta :
Answer:
9pi
Step-by-step explanation:
The ratio between the sector's central angle \purple{\theta}θstart color #9d38bd, theta, end color #9d38bd and 360^\circ360
∘
360, degrees is equal to the ratio between the sector's area, \green{A_s}A
s
start color #28ae7b, A, start subscript, s, end subscript, end color #28ae7b, and the whole circle's area, \blue{A_c}A
c
start color #6495ed, A, start subscript, c, end subscript, end color #6495ed.
Hint #22 / 7
\dfrac{\purple{\theta}}{360^\circ} = \dfrac{\green{A_s}}{\blue{A_c}}
360
∘
θ
=
A
c
A
s
start fraction, start color #9d38bd, theta, end color #9d38bd, divided by, 360, degrees, end fraction, equals, start fraction, start color #28ae7b, A, start subscript, s, end subscript, end color #28ae7b, divided by, start color #6495ed, A, start subscript, c, end subscript, end color #6495ed, end fraction
Hint #33 / 7
\dfrac{\purple{60^\circ}}{360^\circ} = \green{\dfrac{3}{2}\pi} \div \blue{A_c}
360
∘
60
∘
=
2
3
π÷A
c
start fraction, start color #9d38bd, 60, degrees, end color #9d38bd, divided by, 360, degrees, end fraction, equals, start color #28ae7b, start fraction, 3, divided by, 2, end fraction, pi, end color #28ae7b, divided by, start color #6495ed, A, start subscript, c, end subscript, end color #6495ed
Hint #44 / 7
\dfrac{1}{6} = \green{\dfrac{3}{2}\pi} \div \blue{A_c}
6
1
=
2
3
π÷A
c
start fraction, 1, divided by, 6, end fraction, equals, start color #28ae7b, start fraction, 3, divided by, 2, end fraction, pi, end color #28ae7b, divided by, start color #6495ed, A, start subscript, c, end subscript, end color #6495ed
Hint #55 / 7
\blue{A_c} \times \dfrac{1}{6} = \green{\dfrac{3}{2}\pi}A
c
×
6
1
=
2
3
πstart color #6495ed, A, start subscript, c, end subscript, end color #6495ed, times, start fraction, 1, divided by, 6, end fraction, equals, start color #28ae7b, start fraction, 3, divided by, 2, end fraction, pi, end color #28ae7b
Hint #66 / 7
\blue{A_c} = \green{\dfrac{3}{2}\pi} \times 6A
c
=
2
3
π×6start color #6495ed, A, start subscript, c, end subscript, end color #6495ed, equals, start color #28ae7b, start fraction, 3, divided by, 2, end fraction, pi, end color #28ae7b, times, 6
Hint #77 / 7
\blue{A_c} = 9\piA
c
=9π
