The circumference of a circle is [tex]40\pi \text{ cm}[/tex]. A quarter of the circle represents a specific section. Calculate the area of this quarter circle.
Answer (3)
we have to find the radius, how can we got it??
C = 2 π ∗ r
then
40 π = 2 π ∗ r
r = 20 c m
A quarter of the circle will have a surface of a quarter of the circle, there fore
this is the surface of the circle
S = π ∗ r 2
a quarter of it
S 4 1 = 4 1 ∗ π ∗ r 2
then we can replace the value of r
S 4 1 = 4 1 ∗ π ∗ 2 0 2
S 4 1 = 4 1 ∗ π ∗ 400
we can simplify
S 4 1 = 100 π c m 2
2 π r = 40 π c m ⇒ r = 2 π 40 π = 20 S = π r 2 ⇒ q u a r t er : A = 4 1 ⋅ S = 4 1 ⋅ π ⋅ 20 ⋅ 20 = 100 π [ c m 2 ]
The area of the quarter circle, given a circumference of 40 π cm , is 100 π cm 2 . First, we found the radius to be 20 cm and then used the area formula for circles. We took one-fourth of the total area to find the area of the quarter circle.
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