Answer:
12.5 cm²
Step-by-step explanation:
The formula to determine the area of a sector in a circle, given the area of the circle, is:
[tex]\textsf{Area of a sector} = \dfrac{\theta}{2\pi} \times A[/tex]
where:
In this case:
[tex]\theta=\dfrac{\pi}{4}[/tex]
[tex]A=100\; \sf cm^2[/tex]
Substitute the given values into the formula:
[tex]\textsf{Area of a sector} = \dfrac{\frac{\pi}{4}}{2\pi} \times 100\\\\\\\textsf{Area of a sector} =\dfrac{\pi}{4 \cdot 2\pi} \times 100\\\\\\\textsf{Area of a sector} =\dfrac{1}{8} \times 100\\\\\\\textsf{Area of a sector} =\dfrac{100}{8}\\\\\\\textsf{Area of a sector}=12.5\; \sf cm^2[/tex]
Therefore, the area of the sector that subtends an angle of π/4 radians in the circle with an area of 100 cm² is:
[tex]\Large\boxed{\boxed{12.5 \; \sf cm^2}}[/tex]
Answer:
12.5 cm²
Step-by-step explanation:
To find the area of a sector of a circle, we can use the formula:
[tex] \boxed{\boxed{\textsf{Area of Sector} = \dfrac{\textsf{Sector Angle}}{2\pi} \times \textsf{Area of Circle}}} [/tex]
Given:
Area of the circle = [tex]100 \, \textsf{cm}^2[/tex]
Sector angle = [tex]\dfrac{\pi }{4} \, \textsf{rad}[/tex]
We'll use the formula to find the area of the sector.
First, let's find the sector angle in radians:
We have the sector angle as [tex] \dfrac{\pi}{4} [/tex] radians.
So, the area of the sector will be:
[tex] \textsf{Area of Sector} = \dfrac{\dfrac{\pi }{4}}{2\pi} \times 100 \, \textsf{cm}^2 [/tex]
Simplify:
[tex] \textsf{Area of Sector} = \dfrac{\cancel{\pi } }{8 \cancel{ \pi}} \times 100 \, \textsf{cm}^2 [/tex]
[tex] \textsf{Area of Sector} = 12.5 \, \textsf{cm}^2 [/tex]
Thus, the area of the sector is:
[tex] \Large\boxed{\boxed{12.5 \, \textsf{cm}^2}} [/tex]
