# diameter of a circle when area is 1257?

please explain how to get the diameter.

question 2: by what factor must the radius of a circle be multiplied to make the area of the circle 9 times larger?

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• Anonymous

A circle's area is described by the formula A = pi * r^2.

So if we're given an area of 1257, we can simply plug away:

1257 = pi * r^2. Let's divide both sides by pi.

1257 / pi = r^2. Let's get a decent decimal approximation for the left-hand side.

400.116 = r^2. Let's take the square root of both sides.

20.003 = r

So our radius is just a little bit more than 20. We know that the diameter is twice the radius, so the diameter is 40.006, or a little bit more than 40.

For question 2: you can simply work backwards. Say that you have a circle of radius of s that has an area 9 times bigger than a circle of radius r:

9A = pi s^2 = 9 pi r^2

so s^2 = 9 r^2, and taking square roots of both sides:

s = 3r.

So we see that if we increase r by a factor of 3, we're increasing the area by a factor of its square, 9.

Area of a circle = pi * (r)^2 where r is the radius.

find the value of r by solving the equation.

pi (r)^2 = 1257

r = 20

As diameter is twice of radius so the diameter equals 20*2 = 40.

question2 : The radius must be multiplied by a factor of 3 to have the area 9 times larger as in the formula of the area radius is squared and 3 square is 9 therefore it's 3.

The area of a circle is pi*r^2. Let 1257 = pi*r^2 and solve for r.

r = sqrt(1257/pi) and the diameter is just twice the radius.

d = 2sqrt(1257/pi) or approx. d = 20

For question 2, you need to consider the ratio between r and area.

Since area = pi*r^2, you know that for the area to be 9 times larger you need r to be sqrt(9) times larger. (ie 9 = (3)^2)

So, the radius must go up a factor of 3.

1)Well the Area of a circle is (pi)r^2, and the diameter is equal to 2r. there fore we can say that:

1257/(pi)=r^2 then r=square root of 1257/(pi)=20 units, therefore the diameter is = 2x20 = 40 units

2)you first have to times your area by nine =1257x9 = 11313

then once again you put that into your equation:

11313/(pi)=r^2, therefore r = 60 units. to find out how many times the original radius has to be multiplied you simply divide 60 by 20 wich gives you 3 times

• Anonymous
5 years ago

Circle C D=3d {Diameter of circle C is 3 times d} A=pi(r)^2 A=pi(d/2)^2 {diameter is half the radius} A=pi*(3d/2)^2 {C is 3 times the diameter} A=pi*9(d^2/4) {Equation for area of circle C} Circle D d=1 {Chose 1 as diameter because it is easy to work with} A=pi*r^2 A=pi(d/2)^2 A=pi(d^2/4) {Equation for circle D} Solve Plug in one for the diameter for both equations A=pi*9*(1/4)=pi9/4 A=pi(1/4)=pi/4 Divide area C by area D (pi9/4)/(pi/4)=9 times greater

since the equation to get an area of a circle is pi*radius^2

you set that equation so it equals to 1257, so

divide both sides by pi

square root both sides

since radius is half of diameter, you simply multiply the radius by 2 and you will get the answer for part A.

Part B: In this one, they are asking you to find out how much larger is the radius must be in order to get an area nine times of Part A. there is a shortcut way, but i will go the long way this time

so, you multiply the area from part A by 9

1257x9 = new area

then is the same process again, but in this case, i will name the new radius as radius(b) to show the difference between part b and part a

divide both sides by pi

square root both sides

Now you have a new radius that requires to get an area 9 times bigger

you use radius(b) divide it by the radius from part A and you will get the answer.

Cheers

First you use the formula and make an equation(NOTE: I USED 3.14 FOR PIE)

A=pie(r^2)

1257=pie(r^2)

Now solve for the radius that is r.

1257/pie=pie(r^2)/pie

400.32=r^2

Take the sqaure root of both sides and r =:

r=20.01

If the radius is 20.01 multiply it by 2 to get the diameter which is 40.02

d=40.02