Question

WILL GIVE BRAINLIEST PLEASE ANSWER If a circle is dilated by 5/3 and the area of the larger circle is 100pi square cm, then what would be the area of the smaller circle?

Answer 1

Answer:

We have a small circle, that is dilated by a factor of 5/3 creating a larger circle.

If the smaller circle has a diameter D, then after the dilation, the larger circle will have a diameter equal to: (5/3)*D

We know that the area of the larger circle is:

A = 100*pi cm^2.

And the area of a circle of diameter d, is:

a = pi*(d/2)^2

knowing that the diameter of the large circle is (5/3)*D, we can find the value of D.

A = pi*( (5/3)*D/2)^2 = 100*pi cm^2

let's solve this for D:

pi*( (5/3)*D/2)^2 = 100*pi cm^2

( (5/3)*D/2)^2 = 100 cm^2

( (5/3)*D/2) = √(100 cm^2) = 10cm

D/2 = (3/5)*10cm

D = 2*(3/5)*10cm = 12cm.

Then the area of the smaller circle will be:

a = pi*(D/2)^2 = pi*(12cm/2)^2 = pi*(6cm)^2 = pi*36 cm^2

and pi = 3.14

a = pi*36 cm^2 = 3.14*36cm^2 = 113.04 cm^2