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
    1 decade ago
    Favorite Answer

    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.

  • 1 decade ago

    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.

  • 1 decade ago

    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 decade ago

    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

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  • 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

  • 1 decade ago

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

    you set that equation so it equals to 1257, so

    1257=pi*radius^2

    divide both sides by pi

    1247/pi=radius^2

    square root both sides

    sqrt(1247/pi)= radius

    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

    1257x9=pi*radius(b)^2

    divide both sides by pi

    1257x9/pi=radius(b)^2

    square root both sides

    sqrt(1257x9/pi)= radius(b)

    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

  • 1 decade ago

    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

  • 1 decade ago

    area = pi (r^2)

    r = diameter/2

    area = pi (1257^2)/4 = 1240967.6 square units

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