The diameters of two circles are 4cm and 6 cm respectively

Find the ratio of their areas?

areas are proportional to the square of their diameters

area of larger circle : area of smaller circle
= 4^2 : 6^2
= 16 : 36
= 4 : 9

To find the ratio of the areas of the two circles, we can use the formula for the area of a circle:

Area of a circle = π x (radius)^2

The radius of a circle is half of its diameter, so we can find the radii of the two circles like this:

Radius of first circle = 4 cm / 2 = 2 cm
Radius of second circle = 6 cm / 2 = 3 cm

Now, we can find the areas of the two circles using the formula and the radii we found:

Area of first circle = π x (2 cm)^2 = 4π cm^2
Area of second circle = π x (3 cm)^2 = 9π cm^2

Finally, we can calculate the ratio of the areas:

Ratio of areas = (Area of second circle) / (Area of first circle) = (9π cm^2) / (4π cm^2) = 9/4

Therefore, the ratio of the areas of the two circles is 9/4.

To find the ratio of the areas of two circles, we need to divide the area of one circle by the area of the other circle.

The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

Given the diameters of the two circles, we can find their radii by dividing the diameters by 2.

For the first circle with a diameter of 4 cm, the radius is 4/2 = 2 cm.
For the second circle with a diameter of 6 cm, the radius is 6/2 = 3 cm.

Now, let's calculate the areas of the two circles using the formula.

Area of the first circle (A1) = π(2 cm)^2 = 4π cm^2
Area of the second circle (A2) = π(3 cm)^2 = 9π cm^2

The ratio of their areas (R) is given by R = A1/A2.

Substituting the values, we get:
R = (4π cm^2)/(9π cm^2)

The π (pi) cancels out, leaving us with:
R = 4/9

Therefore, the ratio of the areas of the two circles is 4/9.

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