Respuesta :
Part 1)
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=7\ ft[/tex]
substitute
[tex]C=2\pi 7=14\pi\ ft[/tex]
Remember that
[tex]2\pi[/tex] radians subtends the complete circle of length [tex]14\pi\ ft[/tex]
so
by proportion
Find the radian measure of the central angle subtended by an arc with a length of [tex]4[/tex] feet
[tex]\frac{2\pi}{14\pi} \frac{radians}{feet} =\frac{x}{4} \frac{radians}{feet} \\ \\14\pi*x=4*2\pi \\ \\x=8/14 \\ \\ x=0.57\ radians[/tex]
therefore
the answer Part 1) is
[tex]0.57\ radians[/tex]
Part 2)
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=7\ ft[/tex]
substitute
[tex]A=\pi 7^{2}=49\pi\ ft^{2}[/tex]
Remember that
The area of complete circle [tex]49\pi\ ft^{2}[/tex] subtends a length of the complete circle of [tex]14\pi\ ft[/tex]
so
by proportion
Find the area of the sector formed by an arc with a length of [tex]4[/tex] feet
[tex]\frac{49\pi}{14\pi} \frac{ft^{2}}{ft} =\frac{x}{4} \frac{ft^{2}}{ft} \\ \\14*x=49*4 \\ \\x=14 \ ft^{2}[/tex]
therefore
the answer Part 2) is
[tex]14 \ ft^{2}[/tex]
The area of the sector formed by the arc is 14 sq. ft.
What is the circumference of a circle?
The circumference of a circle is equal to 2πr.
where
r is the radius of the circle.
In this problem we have
r = 7 ft
substitute
The circumference of a circle = 2πr = 14π
2π radians subtends the complete circle of length 14π ft.
In order to find the radian measure of the central angle subtended by an arc with 4 ft length.
2π/14π = x /4
x = 8/14
x = 0.57 radians
Part 2)
The area of a circle is equal to πr^2.
where
r is the radius of the circle
A = 49 π sq. ft
The area of the complete circle of 49 π sq. ft subtends the length of the complete circle of 14 π ft.
The area of the sector formed
49 π / 14 π = x/ 4
x = 14 sq. ft
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