what is the area of a circle with a perimeter of 1000m?

Question

dont round the number please.
and what is the formula?
thankx

Answer 1

First, let's relate Area and Perimeter.

The formula for area is

A = &pi r^2

The formula for perimeter is

P = 2 &pi r

In the second formula, let's isolate r

r = P/(2&pi)

Substitute this value into the first formula.

A = &pi r^2
A = &pi [P/(2&pi)]^2
A = &pi P^2 (1/[4 &pi^2] )

Which further simplifies as

A = (1/4) P^2 (&pi / &pi^2 )

And we get a cancellation

A = (1/4) P^2 (1/&pi)

And we know P = 1000, so

A = (1/4)(1000)^2 (1/&pi)
A = ( 1000000/4 ) (1/&pi)
A = 250000/&pi

Answer 2

First, let's relate Area and Perimeter.

The formula for area is

A = &pi r^2

The formula for perimeter is

P = 2 &pi r

In the second formula, let's isolate r

r = P/(2&pi)

Substitute this value into the first formula.

A = &pi r^2
A = &pi [P/(2&pi)]^2
A = &pi P^2 (1/[4 &pi^2] )

Which further simplifies as

A = (1/4) P^2 (&pi / &pi^2 )

And we get a cancellation

A = (1/4) P^2 (1/&pi)

And we know P = 1000, so

A = (1/4)(1000)^2 (1/&pi)
A = ( 1000000/4 ) (1/&pi)
A = 250000/&pi

Answer 3

First, you must find their diameter (d) to get area of circle. You actually can use formula πd to find their diameter (d) OR 2πr to find their radius (r). But I used πd as my calculation to get diameter (d).

You can't say the outer line of circle, 'perimeter'. You should say 'circumferences' that only specialize for circle only.

Circumference of circle : πd
3.142 x d = 1000m
d = 1000 / 3.142
d = 318.27m

Area of circle : πr²
= 3.142 x (318.27m / 2)²
Hence πr² is the area of circle, divide 348.27m by 2 because radius (r) is 2 times less than diameter (d). 2r = d.
= 3.142 x (159.14²)m
= 3.142 x 25323.95m
= 79567.85m²

Use π : 22 / 7 OR 3.142

Answer 4

Perimeter
= 2 x pi x R
= 1000

Therefore, R
= 500/pi m

Area
= pi x R^2
= pi x (500/pi)^2
= 250000/pi m^2

Answer 5

Area of the circle is
A = pi[perimeter/2pi]^2
= perimeter^2/4pi
= (1000m)^2/4pi
= 250000sqm/3.142
= 79567.1546785 sqm.

Answer 6

The perimeter is 2 x pye x radius
Area is pye x radius squared

therefore radius = 1000 divided by 2 x pye = 159.1 metres
therefore area = pye x 159.1 x 159.1 = 79,554.5457 square metres - roughly

Answer 7

79577.47 sq.m.

Perimeter is the circumference, so 2*PI*R = circumference, so R = 1000/ (2*PI) = 159.155.
Area = PI*R^2 = PI*25330.3 = 79577.47 sq.m.

Answer 8

P=Pi*D; where: Pi=3.1416 , D=diameter, P=perimeter
1000=3.1416D; D=318.31m
Area of circle=Pi*Dsquared/4;
A=3.1416*(318.31)(318.31)/4
A=79,577.71 sqm

hope that solves it

Answer 9

Just work backwards

Answer 10

I think you mean circumference

C=2pir
r=C/2pi
r=1000m/(2*pi)

A=pi*r^2
A=3.142*(1000m/(2*pi))^2
A=79577.47155