Question

6. Determine a área de cada setor circular.
a)
3 cm
b)
4 cm
130°
pfvvv é pra agora
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Answer 1

Resposta:

Onde:

π = 3,14

r = raio do círculo

θº = medida do ângulo central

x  = área do arco

a)

$\begin{array}{ccc}\mbox{ \sf {\^angulo } ( \circ) } & & \text{ \sf {\'a}rea ( \sf cm^2 )} \\\sf 360 & \to & \sf \pi r^2 \\\sf 90 & \to & \sf x\end{array}$

$\sf 360^\circ x = 90^\circ \pi r^2$

$\sf x = \dfrac{90^\circ \cdot 3,14\cdot 3^2}{360^\circ}$

$\sf x = \dfrac{90^\circ \cdot 3,14\cdot 9}{360^\circ}$

$\sf x = \dfrac{1\cdot 3,14\cdot 9}{4}$

$\sf x = \dfrac{28,26}{4}$

$\framebox{ \boldsymbol{ \sf \displaystyle x = 7,06 \: cm^2 }} \quad \gets \mathbf{ Resposta }$

b)

$\begin{array}{ccc}\mbox{ \sf {\^angulo } ( \circ) } & & \text{ \sf {\'a}rea ( \sf cm^2 )} \\\sf 360 & \to & \sf \pi r^2 \\\sf 130 & \to & \sf x\end{array}$

$\sf 360^\circ x = 130^\circ \pi r^2$

$\sf x = \dfrac{130^\circ \cdot 3,14\cdot 4^2}{360^\circ}$

$\sf x = \dfrac{130^\circ \cdot 3,14\cdot 16}{360^\circ}$

$\sf x = \dfrac{13 \cdot 3,14\cdot 16}{36}$

$\sf x = \dfrac{653,12}{36}$

$\framebox{ \boldsymbol{ \sf \displaystyle x = 18,14 \: cm^2 }} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo: