Gabe is spending two weeks on an archaeological dig. He finds a fragment of a circular plate that his leader thinks may be valuable. The arc length of the fragment is about 1/6 the circumference of the original complete plate and measures 1.65 inches. A similar plate found earlier has a diameter of 3.14 inches.
Could Gabe's fragment match this plate?
How long would the arc length of a fragment be if it were 1/6 the circumference of the plate?
I have no idea how to start these.
Thanks - and then there's one more if you don't mind.
Toby finds another fragment of arc length 2.48 inches. What fraction of the outer edge of Gabe's plate would it be if this fragment were part of Gabe's plate?
1/4
1/2
2/3
3/4
d = 3.14
pi d = 9.864
2.48 / 9.864 = .251
a quarter of it
To determine if Gabe's fragment matches the plate with a diameter of 3.14 inches, we need to compare the arc length of the fragment to the arc length of that plate.
To find the arc length of a circle, we need to know the circumference and the degree measure of the arc. In this case, we are given that the fragment is 1/6 the circumference of the original plate and its arc length is 1.65 inches.
To find the circumference of the plate with a diameter of 3.14 inches, we can use the formula:
Circumference = π * diameter
Circumference = π * 3.14 inches
Circumference ≈ 9.86 inches
Now, since the fragment is 1/6 the circumference of the plate, we can find the arc length of the plate using the following formula:
Arc Length = (1/6) * Circumference
Arc Length = (1/6) * 9.86 inches
Arc Length ≈ 1.64 inches
Comparing this to the given arc length of Gabe's fragment (1.65 inches), we can conclude that Gabe's fragment does not match the plate with a diameter of 3.14 inches because the arc lengths are different.
In summary, to determine if Gabe's fragment matches the plate, we compared the arc lengths. We found that the arc length of Gabe's fragment is slightly larger than the arc length of the plate, indicating that they do not match.
(1/6)(pi d) =1.65
d = 1.65 (6/pi) = 3.15