Solution and explanation please
Increasing a circle's radius by 20%, causes the circle's area to increase by how much?
A.100%
B.60%
C.44%
D.40%
E. 25%
Cricles
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A=pi*radius squared
If the originial radius equals r, then the area of the circle would be pi*r^2.
Now, if we increased the radius by 20%, the area of the new circle would be pi*(6r/5)^(2)=1.44*pi*r^2. If we compare the area of the circle with radius r to the area of the circle with radius 1.2r, we can clearly see that that area of the circle with radius 1.2r is 44% greater than the area of the circle with radius r.
If the originial radius equals r, then the area of the circle would be pi*r^2.
Now, if we increased the radius by 20%, the area of the new circle would be pi*(6r/5)^(2)=1.44*pi*r^2. If we compare the area of the circle with radius r to the area of the circle with radius 1.2r, we can clearly see that that area of the circle with radius 1.2r is 44% greater than the area of the circle with radius r.
- franciskyle
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A1: (Pi)*(r^2)
A2: (Pi)*(1.2*r)^2 = (Pi)*(1.44)^2
Using the formula:
(X2 - X1) / X1 * 100%
The Pi's & r^2 cancel so:
= (1.44 - 1) / 1 * 100% = 44%
A2: (Pi)*(1.2*r)^2 = (Pi)*(1.44)^2
Using the formula:
(X2 - X1) / X1 * 100%
The Pi's & r^2 cancel so:
= (1.44 - 1) / 1 * 100% = 44%
k. Francis
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R(new) = R + 20% R
where R = original radius
R(new) = 1.2R
And A = pi*R^3
So A(new) = pi*(1.2R)^2
A(new) =1.44 [ pi*R^2]
A(new) = 1.44 A
A(new) increase by =( 1.44-1) *100
= 44% Increase
where R = original radius
R(new) = 1.2R
And A = pi*R^3
So A(new) = pi*(1.2R)^2
A(new) =1.44 [ pi*R^2]
A(new) = 1.44 A
A(new) increase by =( 1.44-1) *100
= 44% Increase