Don't know how to do this geometry question

Question

The area of circle b is 36 times greater than the area of circle a. The radius of circle b is 30. What is the radius of circle a?

Answer 1

The areas of similar figures are in ratio as the square of any linear part.

The area of the larger is 6² time that of the smaller. Therefore its corresponding parts and 6 times as big.

The radius of the small circle is (1/6)30, or 5.

Answer 2

Hi Bryce, the area of a circle is given by the equation: A = pi * r². The radius of the larger circle is 30. 

 

To find the radius of the smaller circle, start by finding the area of the larger circle.

 

Area of larger circle:

 

A_l = pi * 30²

 

A_l ≈ 2827.43

 

The area of the larger circle is 36 times greater than the smaller circle. To find the area of the smaller circle, divide the area of the larger circle by 36.

 

A_s = 2827.43 / 36

 

A_s ≈ 78.54

 

The area of the smaller circle equals pi times the radius of the smaller circle squared. Divide the area of the smaller circle by pi. What is left is the radius of the smaller circle squared.

 

78.54 / pi = 25

 

The radius of the smaller circle is the square root of 25.

 

r_s = √25 = 5

 

The radius of the smaller circle is 5.

 

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