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The diagram shows a 140° sector in a circle of radius 8 units.
140°
8
What is the approximate area of the shaded sector?
0 25 square units
O 67 square units
O
78 square units
156 square units

FIRST TO ANSWER GETS BRAINLIEST The diagram shows a 140 sector in a circle of radius 8 units 140 8 What is the approximate area of the shaded sector 0 25 square class=

Respuesta :

Nayefx

Answer:

[tex] \huge \boxed{ \red{ \boxed{c)78 \: units ^{2} }}}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • circle
  • PEMDAS

tips and formulas:

  • [tex] \rm \:A_{shaded}= \dfrac{\theta}{360} \times \pi {r}^{2} [/tex]

let's solve:

  1. [tex] \sf sustitute \: the \: value \: of \: \theta \: and \: r : \\ A_{shaded} = \frac{140}{360} \times \pi \times {8}^{2} [/tex]
  2. [tex] \sf simpify \: squre : \\ A_{shaded} = \frac{140}{360} \times \pi \times 64[/tex]
  3. [tex] \sf simpify \: fraction: \\ A_{shaded} = \frac{7}{18} \times \pi \times 64[/tex]
  4. [tex] \sf reduce \: 64: \\ A_{shaded} = \frac{7}{ \cancel{ \: 18} \: ^{9} } \times \pi \times \cancel{ 64} \: ^{32} \\ A_{shaded} = \frac{7}{9} \times \pi \times 32\\ A_{shaded} = \frac{224\pi}{9} [/tex]

[tex]\large A_{shaded}\approx 78 \: square \: units [/tex]

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