Respuesta :

Answer:

D. [tex]\frac{3}{8} \pi[/tex]

Step-by-step explanation:

The area of a circular sector is defined as

[tex]A=\frac{\pi r^{2} \theta}{360\°}[/tex]

Where [tex]\theta[/tex] is the central angle and [tex]r[/tex] is the radius of the circle.

Replacing given values, we have

[tex]48 \pi = \frac{\pi (16)^{2} \theta}{360\°}\\ 17,280=256\theta\\\theta = \frac{17,280}{256} =67\frac{1}{2}=\frac{135}{2}[/tex]

But, this angle is in degrees, we know that [tex]\pi = 180\°[/tex]

[tex](\frac{135}{2})\° \times \frac{\pi}{180\°} =0.375 \pi=\frac{3}{8} \pi[/tex]

Therefore, the right answer is D.

abidemiokin

Answer:

The central angle is 3π/8 rad

Step-by-step explanation:

Area of a sector is expressed as [tex]\frac{\theta}{360^{0} } *\pi r^{2}[/tex]

r is the radius of the circle

[tex]\theta[/tex] is the angle substended by the sector

Given Area of a sector = 48πcm²

radius of a circle = 16cm

Substituting the given values in the formula to get [tex]\theta[/tex] we have;

[tex]48\pi = \frac{\theta}{360}*\pi * 16^{2}\\48\pi = \frac{\theta}{2\pi}*(\pi) * 256\\48 = 256\theta/2\pi\\256\theta = 96\pi\\\theta = 96\pi/256\\\theta = 3\pi/8\ rad[/tex]

Otras preguntas