The radii of three concentric circles are 2cm, 3cm and 4cm
Find the ratio of the shaded areas A (the second circle from the inside) and B(the outer circle)
(Hint: don't substitute for pi)
I assume
A is the area between the 2-cm and the 3-cm circles
B is the area between the 3-cm and 4-cm circles.
A = pi(3^2 - 2^2) = 5pi
B = pi(4^2 - 3^2) = 7pi
B/A = 7/5
4:9
7:88
To find the ratio of the shaded areas between the second and outer circles, we need to calculate the areas of both circles and then divide them.
Let's suppose the shaded area of the second circle (A) is represented by A₁, and the shaded area of the outer circle (B) is represented by A₂.
To calculate the area of a circle, we use the formula A = π * r², where A is the area and r is the radius.
Given that the radii of the three concentric circles are 2cm, 3cm, and 4cm, we can calculate the areas as follows:
Area A₁ (second circle):
A₁ = π * (3cm)² = π * 9cm²
Area A₂ (outer circle):
A₂ = π * (4cm)² = π * 16cm²
Now, to find the ratio of A and B, we divide A₁ by A₂:
Ratio of shaded areas = A₁ / A₂ = (π * 9cm²) / (π * 16cm²)
Since we are asked not to substitute for π, we can cancel out the π:
Ratio of shaded areas = 9cm² / 16cm²
Simplifying the fraction, we have:
Ratio of shaded areas = 9/16
Therefore, the ratio of the shaded areas A (second circle) to B (outer circle) is 9:16.