How big was the Flying Saucer?
In the 1951 science fiction movie classic The Thing from Another World, a group of scientists and soldiers discover a recently crashed alien spaceship buried under a few feet of ice near the North Pole. The party spreads out to determine the size and shape of the alien craft under the blurry ice with the following dialogue: "It's perfectly round...yep, we finally found one...a flying saucer." Assuming that each of the 10 person party is exactly 25’ apart along the circumference of the craft, what is the surface area of perfectly flat underside of the flying saucer?
circumference = 10 * 25'
area = circumference^2 / (4 π)
4973.591973
To determine the surface area of the perfectly flat underside of the flying saucer, we need to calculate the area of a circle. We can use the formula for the area of a circle, which is A = πr^2, where A represents the area and r represents the radius.
First, we need to find the circumference of the circle. Since there are 10 people evenly spaced along the circumference, we can divide the total circumference by the number of people to find the distance between each person.
The circumference of a circle is calculated using the formula C = 2πr, where C represents the circumference and r represents the radius.
Let's assume that the distance between each person is d. Therefore, the total circumference (C) can be calculated as follows:
C = d * 10
Now, let's rearrange the formula for the circumference to solve for the radius:
r = C / (2π)
Substituting the value of C as d * 10, we get:
r = (d * 10) / (2π)
Using this value of r, we can now calculate the area of the circle:
A = πr^2
Substituting the value of r, we get:
A = π * [(d * 10) / (2π)]^2
Simplifying the equation, we have:
A = π * [(d^2 * 10^2) / (4π^2)]
Now, we can simplify further:
A = (d^2 * 10^2) / (4π)
Therefore, the surface area of the perfectly flat underside of the flying saucer can be calculated using the formula (d^2 * 10^2) / (4π), where d is the distance between each person.