What is the area? Help please!?

Question

The pendulum is 90 cm long. If it swings side to side through an arc of 20 degrees what is the area?

Please help me i am so confused and i know the formula i just need help doing the probelm so don't give me the formula help

Answer 1

if in degrees

Area of sector = (pi*r^2)(angle/360)

therefore

A = (pi(90)^2)(20/360)
A= 450pi
A=1413.7 ( 1dp ) cm2

Answer 2

imagine a full circle with a radius of 90 cm. This circle is 360 degrees. The 20 degrees covered by the pendulum is a 20/360 or 1/18 of the total area of the circle. The rest should be easy for you to figure out.

Answer 3

um, I think they are asking for the area of the 90 CM arc of 20 degrees right? ok, well, lemme tell ya why the formula works.

Triangles are a peculiar shape. They are easy to determine the size of because of the relationship it has with the other two existing angles. If you know one length of any 3 sides, and an angle of arc, you can figure out the rest. That's where socato comes in, and all that other trig BS.

The pendulum is also swinging on an axis, in radial motion. the actual travel creates a pie shape (like part of a larger circle... think trivial pursuit), so, the trig formulas need to be augmented a bit to compensate for another dimension of motion, in other words, they used what they know about circles, and triangles, and figured out a way to measure them at the same time, given the fact that a 90cm pendulum can only occupy 90cm on one axis, and the 20 degrees of centrifugal motion can only make a triangle so large, that it's only the next logical step to deduce that a triangle fashioned in circular motion, can only occupy one amount of space. Mathematically speaking, it's like finding the given area of a circle that has a 90cm radius, and then figuring out what 20 degrees of that circle would encompass. It might help, to see the mathematical correlation), to convert the 20 degree arc in to a fraction of the 360 degree circle, and seeing the area of the slice of pie as a fraction of the area of that circle That's the formula, and that's how they came up with it. At least they aren't asking you to factor in the actual shape of the pendulum.... welcome to the science of displacement.

Answer 4

The area through which the pendulum moves is a sector of a circle (a "pie") with radius 90 cm and internal angle 20*.

Because 20* is 1/18-th part of a full circle, the area of the sector will be 1/18-th of the area of a circle with the same radius.

The area of a circle with radius 90 cm is
... A[circle] = pi * 90^2 = 8100 pi.

The sector area is 1/18-th of this, so
... A[sector] = (8100 pi) / 18 = 450 pi,
which is approximately equal to 1414 cm^2.

Answer 5

The area of a circle with radius 90cm is pi * (90cm)^2, or 8100*pi cm^2.

A full circle has 360 degrees. This pendulum you're dealing with has an arc of 20 degrees. Hence, the pendulum's swing area covers 20/360 of the circle.

The area is 20/360 * 8100*pi cm^2.
That's 450* pi cm^2, or approximately 1414 cm^2.

Hope that helps!

Answer 6

the shape this is forming is called a sector of a circle. It's simply a fraction of the entire area of the circle, which as you know is πr². In this case, the radius is the length of the pendulum and the fraction of the circle is 20°/360° = 1/18. So the area of the sector = 1/18 * π90² = 450π cm²

Answer 7

A word of caution:

It maybe nothing, but make sure the arc is 20 degrees total from side to side. It's not 20 degrees to just one side, making the total degrees 40 degrees.

It is probably the 1413.7 cm^2 if just 20 degrees like others said.

Answer 8

The area of what? The segment of the circle described if the pendulum made a complete rotation?

π r²/18


That circle would have a radius of 90 cm.

Square that and multiply by pi. That gives you the area of that circle.

A full circle has 360 degrees, 20 degrees. is one eighteenth of the circle, so the area of the full circle divided by 18 gives you the answer you seem to want.