What is the ratio of their areas if two circles have diameters in a ratio of 3/5?

Answer 1

The area of a circle is proportional to r^2 (since the formula is πr^2). Thus, if the ratio of the radii of two circles is 3/5 (the same ratio applies to the radius as to the diameter), then the ratio of the their areas is (3/5)^2 or 9/25.

You can also work this out numerically. As the lowest integer form, circle 1 has a radius of 3 and circle 2 has a radius of 5.

Area of Circle 1 = π(3)^2 = 9π
Area of Circle 2 = π(5)^2 = 25π

Ratio of Areas = Area of Circle 1 / Area of Circle 2
Ratio of Areas = 9π / 25π
Ratio of Areas = 9/25

Hope that helps =)

Answer 2

the ratio of the areas would be the ratio of the squares of the radii.

9/25

Answer 3

Area 1 = π.(d/2)² = π.d² / 4
Area 2 = π.(3d/5)² / 4 = π (9d² / 100)

Area 1 / Area 2 = (1/4) / (9 / 100)
Area1 / Area 2 = 100/36 = 25 / 9
9 Area 1 = 25 Area 2
Area 1: Area 2 = 25 : 9

Answer 4

p=r^2*pi

so its 9/25

Answer 5

a/A={pi(d/2)^2}/{pi(D/2)^2}
=d^2/D^2
=9/25