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Juan drew a circle with a radius of 4 cm. He drew two radii that formed a 150 degrees angle. He used the steps below to find the area of the sector formed by the 150 degrees angle.

Area of Circle: A = pi r squared = pi 4 squared = 16 pi

Area of Sector:StartFraction 16 pi over a EndFraction = StartFraction 150 over 360 EndFraction. 150 a = 5,760 pi. A = 38.4 pi.

What error did Juan make in finding that the area of the sector is 38.4 pi centimeters squared?
He found an incorrect area for the entire circle.
He set up the proportion incorrectly.
He solved the proportion incorrectly.
He used the area of the circle instead of the circumference.

Please help quickly Will give brainliest if i can Juan drew a circle with a radius of 4 cm He drew two radii that formed a 150 degrees angle He used the steps b class=

Respuesta :

musiclover10045

Answer:

He set up the proportion incorrectly. The area of a sector is the area of the entire circle x the proportion of the angle.

Area of sector = 16PI x 150/360 = 20.94 square cm.

olayemiolakunle65

Answer:

He set up the proportion incorrectly.

Step-by-step explanation:

Juan was able to determine that the area of circle = 16[tex]\pi[/tex].

Area of a sector = (θ/[tex]360^{0}[/tex]) × [tex]\pi r^{2}[/tex]

⇒ Area of a sector = (θ/[tex]360^{0}[/tex]) × area of circle

                               = (θ/[tex]360^{0}[/tex]) ×16[tex]\pi[/tex]

where θ is the value of the angle formed by the two radii and r is the value of the radius.

So that,

Area of a sector  = [tex]\frac{150^{0} }{360^{0} }[/tex] × 16[tex]\pi[/tex]

                            = 6.67[tex]\pi[/tex]

The area of a sector is 6.67[tex]\pi[/tex] [tex]cm^{2}[/tex].

Juan made an error by setting up the proportion incorrectly.