Geometry problem?

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Find the area of a circle whose radius is 1/pi is: (exact value)

By exact value, I believe the answer should have pi in it, not multiplied out with just 3.14, if that makes sense...
Thank you!

Answer 1

The area of a circle is pi(r)^2

If the radius is 1/pi

The area is pi(1/pi)^2

= pi (1/pi^2)

= 1/pi

The area is 1/pi square units.

Answer 2

There are some things you need to become familiar with.

The perimeter of any object, no matter how irregular, is equal to the sum of the lengths of its sides. For a circle, which has either infinite sides, or no sides, depending on your viewpoint, the area is C = 2πr where "C" is circumference.

Area of a parallelogram (including rectangles and squares)
A=lw [Area = length multiplied by the width. In the case of a square, the length and height are the same, so A=l²)

Area of a trapezoid. A trapezoid has two sides parallel.
A= (½)h(a+b) where h is the perpendicular distance between the two parallel sides, and the lengths of the parallel sides are a and b. This works for a triangle for which the length of one of the parallel sides (a vertex--the point farthest away from the side you're calling the base) =0 so that A=(½)hb.

Area of a circle with radius r. You should know that the radius = ½ the diameter.
A = πr² Any numeric value you come up with will be an approximation because nobody knows the exact value or π, Usually it's approximated by 3.14 or 22/7.

Volume of regular figures (cylinders, boxes, prisms) is B=Ah where A is the area of the base, and h is the length of the object. For example, the volume of a cylinder would be V=πr²h. Note, in the trapezoid smf triangle, be careful not to confuse the height of the base (h) with the length of the object (h). Just find the area of the base and then multiply that by the length.

Now, what was the formula for the area of a circle with radius 1/π ? A=πr²?
Substituting 1/π for "r" in the formula
A=π(1π/)²
= (π)(1/π)(1/π) because (1/π)²=(1/π)(1/π)
=(1)(1/π) because (π)(1/π)=1
=1/π because 1(1/π)=1/π

Now, if you want a numeric approximation, you can use whatever approximation of π you wish to approximate 1/π, and you can use a calculator or a spreadsheet.

Answer 3

area of a circle is equal to pi * r^2 where r is the radius

your radius is 1/pi so r^2 = 1/pi^2

now area is pi * 1/pi^2 = 1/pi

thats an exact value...its interesting because its a circle whose area is equal to its radius...cool

Answer 4

pi/pi squared