The radius of the small circle A is one-half the radius of the large circle B.WHat is the ratio of the area of the small circle to the area of the large circle?
Why not just pick two values of r
say: r = 3 and r = 6
area of small = 9π
area of larger = 36π
You will find that the ratio of small circle : large circle = 1 : 4 , no matter what numbers you pick
To find the ratio of the area of the small circle A to the area of the large circle B, we need to compare their areas.
Let's denote the radius of the small circle A as r and the radius of the large circle B as R.
Given that the radius of A is one-half the radius of B, we have r = (1/2)R.
The area of a circle is calculated using the formula A = πr^2.
So, the area of the small circle A is Aa = πr^2 and the area of the large circle B is Ab = πR^2.
Substituting r = (1/2)R into the equations, we get Aa = π(1/4)R^2 and Ab = πR^2.
To find the ratio of their areas, we divide the area of the small circle A by the area of the large circle B:
Ratio = Aa / Ab = (π(1/4)R^2) / (πR^2)
Simplifying the expression, we get:
Ratio = (1/4) / 1 = 1/4
Therefore, the ratio of the area of the small circle to the area of the large circle is 1:4 or 1/4.
To find the ratio of the area of the small circle to the area of the large circle, we first need to understand the relationship between the radius of the two circles.
Let's say the radius of the small circle A is denoted as "r", and the radius of the large circle B is denoted as "R". It is given that the radius of circle A is one-half the radius of circle B, so we can write this relationship as:
r = (1/2)R
Now, let's find the formula for the area of a circle. The area of a circle is given by the formula:
A = πr²
where "A" represents the area, "r" represents the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.
Using this formula, the area of the small circle A is:
A₁ = πr²
And the area of the large circle B is:
A₂ = πR²
Now, substitute the relationship r = (1/2)R into the formulas for the areas:
A₁ = π((1/2)R)²
= π(1/4)R²
= (1/4)πR²
A₂ = πR²
The ratio of the area of the small circle to the area of the large circle can be calculated by dividing the area of the small circle by the area of the large circle:
Ratio = A₁ / A₂
= ((1/4)πR²) / (πR²)
= (1/4)
Thus, the ratio of the area of the small circle to the area of the large circle is 1/4.