Question 11 [Total Marks 5]
The egg displayed is composed of 4 arcs from 4 sectors.
The arc AC has centre B.
The arc BD has centre A.
The arc AB has centre O.
The arc CD has centre E.
The radius of the central circle is 1cm.
OE and OB form a right angle.
Calculate the perimeter of the egg.
What is the answer??
(3-rt2/2)pi
To calculate the perimeter of the egg, we need to find the lengths of each of the four arcs and add them together.
Given that the radius of the central circle is 1cm, we can assume that OB and OE are both 1cm long.
Since OE and OB form a right angle, we can conclude that triangle OEB is a right-angled triangle.
Applying the Pythagorean theorem, we can find the length of the hypotenuse EB:
EB^2 = OE^2 + OB^2
EB^2 = 1^2 + 1^2
EB^2 = 2
EB = √2
Now, let's consider the four arcs: AC, BD, AB, and CD.
1. Arc AC:
The arc AC has center B, and we know that the radius of the central circle is 1cm. Since AC is a quarter of the circumference of the central circle, its length can be calculated as a fraction of the circumference:
AC = (1/4) * 2πr
AC = (1/4) * 2π * 1 cm
AC = (1/2)π cm
2. Arc BD:
The arc BD has center A, and using the same logic, its length can be calculated as:
BD = (1/4) * 2πr
BD = (1/4) * 2π * 1 cm
BD = (1/2)π cm
3. Arc AB:
The arc AB has center O, which means it is half of the circumference of the central circle:
AB = (1/2) * 2πr
AB = (1/2) * 2π * 1 cm
AB = π cm
4. Arc CD:
The arc CD has center E, and applying similar calculations, its length can be found as:
CD = (1/4) * 2πr
CD = (1/4) * 2π * 1 cm
CD = (1/2)π cm
Now, let's add up the lengths of all four arcs to find the perimeter of the egg:
Perimeter = AC + BD + AB + CD
Perimeter = (1/2)π + (1/2)π + π + (1/2)π
Perimeter = (3/2)π + π
Perimeter = (5/2)π cm
Therefore, the perimeter of the egg is (5/2)π cm.
To calculate the perimeter of the egg, we need to find the lengths of each arc and add them together.
Let's start by analyzing the given information:
1. The radius of the central circle is 1cm, which means the distance from the center of the circle (point O) to any point on the circle is 1cm.
Since the radius is 1cm, the circumference of the central circle is given by 2πr = 2π(1) = 2π cm. (Equation 1)
2. It is given that arc AC has center B. This means that the distance from the center of arc AC (point B) to any point on arc AC is the same as the radius of the central circle (1cm).
3. Similarly, arc BD has center A. Therefore, the distance from center A (point A) to any point on arc BD is also 1cm.
4. The arcs AB and CD have centers O and E, respectively. However, the distances from their centers to points on the arcs are not provided.
Now, let's calculate the lengths of each arc:
- Arc AC:
Since the radius of the central circle (OB) is 1cm, the length of the arc AC is equal to the circumference of the central circle (2π cm) minus the length of the arc AB.
Arc AC = 2π - arc AB
- Arc BD:
Similarly, the length of the arc BD is equal to the circumference of the central circle (2π cm) minus the length of the arc CD.
Arc BD = 2π - arc CD
- Arc AB and Arc CD:
To calculate the lengths of arc AB and arc CD, we need more information about their centers and the corresponding radii.
Unfortunately, without the specific values or angles, we cannot determine the lengths of arc AB and arc CD, and therefore, we cannot calculate the perimeter of the egg.
So, in this case, the perimeter of the egg cannot be determined without additional information.
starting at A, please list the points clockwise in order.
Are any of the arcs more than 180° ? That is, major arcs, instead of minor arcs.
what do you mean by "central circle"? Is it connected to the egg in some way?